Solving a quadratic by completing the square
ฝัง
- เผยแพร่เมื่อ 8 ก.พ. 2025
- 👉 Learn how to solve quadratic equations by completing the square. When solving a quadratic equation by completing the square, we first take the constant term to the other side of the equation and create a perfect square trinomial with the quadratic term and the linear term. If the coefficient of the quadratic term is not 1, we factor out the coefficient before creating the perfect square trinomial.
The perfect square trinomial is created by adding to both side of the equation, the square of half the coefficient of the linear term (the term whose variable is not squared). Note that you must account for the factored out value when adding the square of half the linear term to the other side of the equation. Then the perfect square trinomial is evaluated and then we solve for the variable to get the solution(s) to the quadratic equation.
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✅How to Solve a Quadratic by Completing the Square
• How to Solve a Quadrat...
✅Solve a Quadratic by Completing the Square | Fractions
• Solve a Quadratic by C...
✅Solve a Quadratic by Completing the Square | -x^2+bx+c
• Solve a Quadratic by C...
✅Solve a Quadratic by Completing the Square | 2x^2+bx+c
• Solve a Quadratic by C...
✅Solve a Quadratic by Completing the Square | ax^2+bx+c
• Solve a Quadratic by C...
✅Solve a Quadratic by Completing the Square | x^2+bx+c
• Solve a Quadratic by C...
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• Solve a Quadratic by C...
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#Solvequadratics #completethesquare #brianmclogan
Quick Guide to Completing the Square - th-cam.com/video/MveZ6dyKMuA/w-d-xo.html
One thing I would do differently is I would do a times c which would be much easier to solve
Quick?
Thanks. I didn't care about your actual numbers. I forgot how the method worked. Been s few years since my math degree. OK, I guess I could prove the quadratic formula again. Makes sense
I was impressed by the teacher, Mr. McLogan, who kept stopping to answer a question from a student. I bet he is a great teacher. Also, too many math teachers skip steps because the skipped step is "obvious." Of course, it it obvious to highly intelligent people with a gift for math. Mr. McLogan did all the steps. Very well done!
THISS!!! They always skip explanations
@@Abc-xm8pb Right- like they combine 3 steps like its normal. Im in a new district and in a grade above what I’m supposed to be in (so I didn’t learn what they did/what they did) and its so annoying because I get lost so fast. Then my parents get mad at ME for not paying attention in class when I am and asking questions but shes so hard to approach-
Oh yeah, shows he has the patience to work the problem step by step.
Thing is tho since iam used to teacher skipping obvious steps when they actually go through the obvious steps i get more confused than if they dont go through obvious step
Theres no such thing as someone who is gifted at something they need to learn
Not the hero we deserved, but the hero we needed.
This man is carrying me through my college courses.
Thank you Mr. Brian McLogan. I owe you bigtime!
batman revealed????
Not the hero we deserved, but the hero we needed.
This man is carrying me through my college courses.
Thank you Mr. Brian McLogan. I owe you bigtime!
It makes me proud to know I can understand a little bit of college material when I’m only in middle school 😅
Updated Explanation - th-cam.com/video/JtUq2PojEWg/w-d-xo.html
Download the Guide (PDF) - www.brianmclogan.com/SolvebyCompletingthesquarepdf
Purchase the Answers (PDF) - brian-mclogan.creator-spring.com/listing/solve-by-completing-the-square
I got a 100% in 3 of my most important tests because of you! Thank you and keep making more videos like this!
Awesome Aditya! happy to be there for you
i’m so cooked
💀
Same
Me too I got a test tmr it’s wraps
Same thing my boy
@@AbdullahOubouziane i got a quiz tmrw lmfao we r all cooked
There are 3 methods:
1) factorise, if possible (by far the easiest, when possible).
If not 1), then
2) use the formula for roots of a quadratic equation (x = -b +/- etc)
3) complete the square, which is preferred when the coefficient of x is an even number.
{Completing the square in such a case also reveals the co-ordinates of the Vertex
eg with y = x^2 -4x -2 , completing the square yields
y = (x -2)^2 - 6 which has a minimum value of -6 when x = 2.
The Vertex is the point (2, -6)}, which also reveals the Axis of symmetry ie the line x = 2.
A useful "test", so to speak, is to get students to work out the discriminant (b^2 - 4ac) which always tells the student a lot about the quadratic. Evaluating the discriminant is never a waste of time, because
--- it's good mental gymnastics ie brain exercise, with the additional caveat of the dangers of negative numbers, and
--- prepares the student for the type (and graph) of the quadratic they are dealing with.
eg when b^2 - 4ac = 0, there is only one real root, which means the quadratic itself is a perfect square. Useful for predicting solutions and sketching graphs.
In the case above, b^2 - 4ac = 81, which number is a perfect square.
When the discriminant is a perfect square, the quadratic has 2 real roots, which means that it can be factorised. ALWAYS.
2x^ + 7x -4 = 0
==> (2x - 1)(x + 4) = 0.
x = 1/2 and x = -4.
The question itself confuses me, so with respect:
Mr. McLogan, why would you get students to complete the square on
2x^2 + 7x -4 =0, unless it was specifically to teach/reinforce the technique of completing the square itself?
Completing the square on a Quadratic that can be factorised is unnecessarily complex and takes more time than factorising.
Flexibility is key and in Exams/Tests, a time-saver.
thank man
thanks man
In some questions in a test or exam, the question specifically asks you to solve by completing the square that's why he's teaching this more complicated methods
Use desmos chat
In high school I decided not to pay attention in school, starting hanging around the wrong people and eventually after high school got my life in check and decided to go to college. I struggled so hard in math because of my HS situation. Your videos have helped so much. Today I can say I've graduated with a B.S in Exercise Science and on my way to getting a Doctorate.
Love it, congrats to you
@@brianmclogan it’s really cool that you are still replying to comments even after 10 years
Just curious, are you in PT school? Lol I’m thinking of doing exercise science, how was it?
This video was recorded in 2012 but it still helped me a lot even in 2021 at varsity...Thank you so much, Sir. May God bless you.
10 years later and this video still helps people like me - thank you for being a great teacher Mr.Logan
Math is the reason i became a Chef. Just cut, chop, cook and present. EASY.
LMFAO 😁 😂❤️💚 💛 hahahaha
well when you put it like that...
but I'm sure being a chef is a little more nuanced than that buddy ;)
@twistedblktrekie you win this time
@@turtletube I- did someone post that on your comment. FYI don’t let ppl get to u lol. Nobody asked and? Who cares it’s the internet ppl can comment what the fuck they want
Funny
As someone who gets to explain this several times a year, I appreciate you taking the time to do this in front of a camera. Not sure why you didn't simplify that 2 out like you wanted to at the beginning, though. Simplifying as much as possible as early as possible cuts down on sloppy errors later.
I was literally screaming that at the video from the start. He made this overly complicated.
I know. While he was doing all that, I had already solved the equation in my head using the quadratic formula, thus getting {2, -4} as my answer.
The fact he did not simplify offered a refresher course though. Now I don't have to go and learn fractions operations all over again. In structural design fractions are very common and you have to get used to them. 😑 Can't just ignore them as that would prove fatal. For me the video was a blessing.
@Matt Slupek 1/2, not 2.
I’ve been out of school for a very long time and have had a successful career in medical device engineering. I’ve honestly forgotten how good it was to have a great math teacher. I was fortunate to have quite a few of them and you are one of the good ones. When you are having a though day, remember you are making a difference!
I wish I was part of the class being taught 😭😭❤
well you have the next best thing I guess, the recorded version
After finish giving a lecture on solving a quadratic equation.
Teacher: Any question?
Student raises hand.
Student: So a lot of it is algebra stuff.
haha yes
Solve almost any calculus problem in 10 steps and it's almost always: 5 steps of algebra, 1 step of calculus magic, 4 more steps of algebra.
Mastery of Algebra is so incredibly fundamental to all higher math.
and basic operations such addition and subtraction
very nice, you can also check out on my channel for more mathematics contents
College calc student here. You'll be doing this stuff all over again lmao here I am trying to refresh. Brings back memories of high school haha
Lots of repetition👏👏👏
stop looking at comments and study 😂
lol...
this is hard :(
Very funny
s
Jennifer Pacheco read my comments because the teacher is not teaching you the right way. It took him 3 minutes to solve a 30 seconds question!
hahahaha this is very funny
I always wished he was my secrete person which I only knew him but again, he admires and draws paths for other human beings. He deserves more than what he has.
Thanks you, you made me understand this material way better than my teacher .
yup, same for me
This man is not being the best in the world, but the best for the world.
see this is why i really dislike math he filled up the whole board for one problem one freaking problem!!!!
Lame no one cares
@@ccsddhdnc8548 your right bro whyd i even write this comment
he made this more complicated than it needed to be tho
@@ccsddhdnc8548 smh ❄️
Math is the language of numbers. If you want to be good at it, you first have to know how you, as an individual, learn it. I, for example, don't learn math in the same way I do other subjects. I actually had to research different learning styles and try them out -- until I found what worked for me (visual and conceptual math learner).
Basically, I need to understand the mathematical logic and concepts behind what I'm doing in order to grasp algorithms. I will take a long problem, break it down to its core concepts and study each of them -- until I've mastered them. I also learn faster from video (taps into multiple senses at the same time) than I do books.
Even though video helps me to learn faster, I will still take notes (also helps me to learn/remember things). After I have watch videos on the core concepts (typically twice each) and have taken notes, I will attempt to do problems on my on -- starting with simpler ones and working up to hard ones.
If I notice that I keep messing up in a certain spot, this lets me know I need to review a concept. I do this until I feel comfortable -- and until I can fully explain things to myself. This includes the concepts, logic, and various approaches. Looking up various approaches (and videos by different people) can help you to gain a deeper perspective. I've found that no one instructor answers all of my questions.
Such an amazing instructor. for someone scared of fractions, professor mclogan made me understand it so easily
I saw this video unexpectedly and I was shocked. Those steps are really complicated. I
was taught by my teachers to follow very simple steps when I was in grade 8. The steps are given below.
2x2+7x-4=0
2x2+8x-x-4=0
2x(x+4)-1(x+4)=0
(x+4)(2x-1)=0
x+4=0 or 2x-1=0
x=-4 or x=1/2
ලයනල් ගුණතිලක your method is solving using factorising, not by completing the square. This video is about completing the square.
your method is simple n correct but it is not completing the square. You cannot have 2x2 in completing square
MUCH EASIER TO DIVIDE EVERTHING BY 2 AT THE BEGINNING!
except 7 is not divisible by 2
ibrahim kuyumcu is that a whole number?
Tomato, Tomahto
so u just get 7/2. i didit that way and got the same answer without confusing myself.
@@brianmclogan Divide it and leave it as a decimal. 3.5
Why is this 500 times more efficient than what I was shown in class? I thank you monumentally for this.
I appreciate you for taking your time in doing this on carmera . Making it so simple
Hi Brian. Many thanks for this ! Just one thing puzzled me ... when you had 2(x^2+7/2x)=4 why didn't you divide both sides by 2 to leave x^2+7/2x=2 ? This would give easier numbers to work with later on.
not sure, great idea will look into trying it next time
what's your opinion in my video ?
pls write to me
You could have done it this way. But when finding the vertex form it is much more similar to what the guy in the video has done.
[I believe] it all depends on the reason you are completing the square. If your goal is to solve (find the value(s) of x that satisfy the equation) 2x^2+7x-4 = 0 then dividing by 2 will not change your final solution (as long as you divide both sides by 2). However, if your goal is to eventually graph the function, you will change its shape if you divide by 2. I believe this is why most textbooks (and teachers) default to the type of procedure shown in this video; to prevent you from changing the shape of the graph.
Multiplying or dividing both sides of an equation does not change the graph. y=x looks exactly like y/2 = x/2. And he does divide both sides by 2, he just does it on step 8 instead of step 2.
Thanks for the help. My son was struggling with this. I’ve had 2 years of calculus 20 years ago but needed to dust off the cobwebs. Watched your video, showed my son how to do them. Got to bond with and teach my son at the same time. Thank you for this ❤
Just to point out, you don't have to eliminate the x^2 coefficient. You could double instead to make 4x^2 + 14x = 8. Then to make a perfect square on the LHS: 4x^2 + 14x + 49/4 = 8 + 49/4, etc. A grid method is helpful to see how this works.
that is correct
Wow your smart too
2x² + 7x - 4 = 0
Step 1 : multiply 2 with 4 ; 2×4= 8
Step 2: calculate factors of 8 which can satisfy 7 while add and subtract. They're +8,-1
Step 3: write the equation into 2x² + 8x -1x -4 = 0
Step 4: write it in a simple form: 2x(x+4)-1(x+4) = 0
=> ( 2x-1)(x+4) = 0
=> x = 1/2, -4
That's it
You have the patience of a saint. It's good to see a gifted teacher teach.
I learned one year ago
In Grade 10, 2018. NOW I'm in Garde 11 and its up to us chapter conicsection, especially topic of propola (h,k), From somalia.
I liked this teacher very much wlh
Go,head teacher
Do you know de wae to solve this in a simpler way
Yes, pro i can solve the simple
Way that teache me my teachrr
I don't remember being taught this overly complicated method. Every math class I had from junior high through college used the factoring method which is way faster. I solved this problem in 2 lines.
Really he overkilled such a simple thing.
You need all the three methods, in case you are asked to used a specific method.
Again, some quadratic questions cannot be solved by factoring, which is why you need to learn the use of quadratic formula (the almighty formula) and the method of completing the square.
@@osumanuabubakar9557 Yes! After further thought I realized I was way off base in my comment. After these students learn all 3 methods, they then could chose the best method.
I fall asleep everyday in math class (7th period) and I never know what we’re learning. Thanks to you Mr. McLogan, I’m not behind in class! In fact, I get better math grades than my friends.
I am in class and already lost so I raise my hand.
Brian McLogan (Teacher):
"Yes, Kamikaze you have a question?"
Kamikaze (Me):
"Yessir, just one."
Brian McLogan:
"What is your question?"
Me:
"Can I transfer out of this class and sign up for Shop instead?"
"sure" haha
Now I understand where the complete the square is
x^2 + 7/2 + 49/16
2(x+7/4) (x+7/4)
Thanks sir, You Legend
Thank you! I'm a 7th grader being forced to take algebra lessons that are really hard to understand. With your video, you really helped me a lot and I appreciate it. Keep up the good work!
How is algebra hard to understand, I'm also a 7th grader and I know calculus 1
@@SierNotsruhtsure kid💀
@@SierNotsruht ur profile pic clearly reflects u. not everyone is as "smart" as u. also who asked idiot?
@@SierNotsruht your a 7th graders with a nerd profile picture, just gonna guess that when you say you "know" calculus 1, you just mean you've seen a 10 minute video about it on TH-cam and consider that enough to act like an expert.
your pfp says it all nigga
@@SierNotsruht
This isn't the only way to solve this equation.
That is is what is so beautiful about math. Someone will eventually
see a new way to solve an impossible math problem.
Its the reason why I scored much higher by showing my work
for all my calculus exams. I often started any number of approaches
to solving integral and derivative problems, and abandoned them too quickly.
I came to a point where in my pursuit of quicker & easier solutions
to math problems gave me a distinct advantage for which my instructors
found a way to give me credit where it was due.
This man's convoluted solution to a simple problem was a good example of
how to lose most students, but some students may have found the solution
as such was and is an epiphany.
Brian why did you make things complicated?
2xx+7x-4 = 0
or, 2xx+8x - x-4=0
or, 2x(x+4)-1(x+4)=0
or, (x+4)(2x-1)=0
so it is x=-4 or x=1/2.
Follow factorization method
2x^2+7x-4=0
2x^2+8x-x-4=0
2x(x+4)-1(x+4)=0
(2x-1)(x+4)
X=1/2 or X=-4
This has me so lost man.
There are easier methods for solving a quadratic - Besides he may have been showing this particular example to students for years
He makes it very complicated but it’s very easy if you use the formula delta = b square-4 ac ..a=2 , b=7 and c = - 4 .. so delta = b square - 4 AC = 49 -( 4 times 2 times -4 = 81 .. then x1 = (- b - square root of delta )all divided by 2A .... square of delta = square root of 81 =9 .. x1 = (- 7 - 9 ) divided by 4 =-16 /4 =- 4 ..X2 = (-B + square root of delta ) /2A = (-7 + 9 ) / 4 = 2/4 = 1/2 ..
@@chokrimzoughi3330 sorry I don't speak Brazilian Portuguese.
i pretty much think that is this mans theory.....
I can’t do this kind of math AT ALL. That’s why I’m a welder and not an engineer.
as a 9th grader studying for midterms, i can confidentely say this has prepared me better than the entire unit my teacher *tried* to teach us
Did this IN MY HEAD, in under 10 seconds, at age 82 ( in 12 days time !) : WHAT A LOT of work to do on a SIMPLE Quadratic !!!! :o
Before I had a real struggle with this but when I found your video it taught me more and went more deeper into how I solved by completing the square. Now I have my midterm coming and I feel confident after seeing this. Thank you.
this man is every race in one
wasn't ready for that one!!! LOL!!!
Ax^2 + Bx + C = 0
Multiply A and C, then find multiples of the product that can be added or subtracted to equal B.
2x^2 + 7x - 4 = 0
2 × 4 = 8
Multiples of 8 are:
1 * 8 = 8
2 * 4 = 8
4 * 2 = 8
8 * 1 = 8
8 - 1 = 7
So the factor of the equation is
(2x - 1) (x + 4) = 0
To check, FOIL to get back to original equation.
2x * x = 2x^2
2x * 4 = 8x
-1 * x = -1x or -x
-1 * 4 = -4
2x^2 + 8x - x - 4 = 0
Add like terms
2x^2 + 7x - 4 = 0
It matches... :D
Set each parenthesis equal to 0 and solve for x:
2x - 1 = 0
2x = 1
x = 1/2
x + 4 = 0
x = -4
Therefore, x = 1/2 and x = -4.
This isn't completing the square, but once mastered, it is way faster.
I look at the equation and my brain says (2X - 1)(X + 4)=0. So, the roots are X = 1/2 and X= -4.
Me too
Same here. The entire time I’m like I did this in my head in 30 seconds, why such a long video lol.
me too
I guess he’s teaching a theory for when the result isn’t so deducible. But yes this problem only actually take a 10sec by factoring the equation
What if the equation is more complicated, that you cannot really on your education and experience with such equations to be able to figure it out on site. He's showing a method to solve it, which can be used for even more complicated equations.
Watching this plodding process, sprinkled lightly with logic here and there on an ad hoc basis I can readily understand why most people hate math. It's not as if quadratic equations are introduced immediately in an introductory algebra course. Before tackling quadratic equations a pre-req would be to be introduced to some identities such as:
( x - A )^2 is identical to x^2 - 2*A*x + A*2.
The RH of this identity is a quadratic expression similar in appearance to the typical quadratic we are being asked to solve by the " completing the square " method. The latter process then will depend on this identity. This is a clear indicator that the first step in solving by completing the square should be to reduce the coefficient of x to 1. This, in the presentation, was sloughed over and presented as a " rule ".
The point I'm trying to make here is that since quadratic equations appear in an algebra course only after some preliminary work on identities and factorization why not use this algebraic knowledge to solve a quadratic instead of the seat-of-the-pants ad hoc process presented here ?
In the real world I have never encountered a case where " completing the square " is a useful approach, and cannot understand why it is even mentioned in an introductory course.
This is why i cheated in HS.
haha okay
you're pathetic if you can't do simple algebra. Congrats with your future as a cashier lmao
It's so easy I solved it less than 2 minutes
+Kevin Contreras Hey! Squidward is doing great as a cashier.
I'm doing great as a business man, trust me, you won't be using this math after high school
Very impressive teaching... I did the problem prior to watching the video. I used the quadratic formula and got the same answer with far less complications.
you just need to factorise the equation and you get the same result only in two lines thanks soo much
This is the only video that actually made me understand this concept! Thank you so much!!!!!!!
i’m in year10 and i’ve just come across learning something like this. it’s the first time I know that maths is going to take a turn. and your video helped explain everything !! thank you! :)
Cheers, Keep working hard
Hi Army Stream ON
Wow
PRACTICE MAKES PERFECT. AND NOBODY IS PERFECT, SO WHAT IS THE POINT OF PRACTICING?
You are either in England, Oz, or NZ. "maths". "year 10".
I learnt many things from your videos and completed my GED , and now I am in India . I sent my wishes to your daughter, when she is born last year ( you informed that ) How is your sweet baby . My wishes to little angel , God bless her.
congrats to you, our little girl is doing great!! thanks for following up
This is the longest possible way of doing this question. There is a sooooo much easier and shorter way. I don't know what it is but american people do it this way. Teachers in England have a method that takes one quarter of this much time. Or it's just that in years higher than me they do it this way. But all I know is that it could be done much quicker.
this is me breaking it down slowly for my students. In my pre-calculus class we go much faster. Not sure if it is the same way you are describing though
TELL ME PLEASSSSEEEEEE
ax^2+bx+c -------> 2x^2+7x-4=0
Δ=b^2-4ac -------> 7^2-4(2*(-4))= 49+32=81
√Δ=√81=9
x=(-b-√Δ)/2a and x=(-b+√Δ)/2a -------> x=(-7-9)/4=-16/4=-4 and x=(-7+9)/4=2/4=1/2
Say we have: 2x^2-8x-4=0
1) Factorise and take the coefficient of a out. (Don't factorise the c, the last number)
2(x^2-4x)-4=0
2)Complete the Square of the equation in the bracket.
2[(x-2)^2-4]-4=0
3)Expand, but only the last number in the squared bracket.
2(x-2)^2-8-4=0
4)Simplify and solve.
2(x-2)^2=+12
Divide by 2
(x-2)^2=+6
Root
x-2=+or-√6
add 2
x=2+√6 OR x=2-√6
This obviously works for all equations when the coefficient of a is not 1. I used 2x^2-8x-4=0 Because it was easier to write in the comments than the equation in the video.
Brian McLogan no it's awful and confusing. Check out yaymath with Robert ahdoot.
Explained very clearly
Good Math teacher, you young people should be glad to have him.
Quadratic formula seems far easier. ... for me at least... what is the purpose of using this method? Can't the Quadratic Formula just be used each time?
In most cases, the question will ask to see your work (the process of how you got the answer)
I'm just wondering. Wouldn't it have been easier/faster, after factoring out the 2, to divide both sides by 2, at that point?
Divide by 2 and then use the p-q-formula or Quadratic formula
NO! Cuz then on the right side you are doing "0/2" which is a NO-NO!! Rights side still 0, but you've changed the left side. It will mess everything all up, and screw you up.
Or are you talking about AFTER he adds 4 to both sides?
@@aspenrebel 0/2=0. You're not dividing by zero. In other words,
2x^2+7x-4=0
2(x^2+(7/2)*x-2)=0
x^2+(7/2)*x-2=0
x^2+(7/2)*x=2
At this point, we have already gotten a coefficient of 1 on the x^2-term, and then moved the constant term to the other side of the equation, so now, we can go down the route, where we complete the square.
@@herbcruz4697 ok, I guess I was thinking dividing both sides by "x", would give right side of 0/x. Nevermind.
Absolutely agonizing but you gave me a lot more help than my college did, thank you!
07:02 that sudden change of expression, yet I love how you teach. please keep it up! I'm having a hard time with my calculus, I find this channel to be very very helpful for the journey.
happy to be there to help you Erloel!
Oh! change of expression IN HIS FACE!! I thought you were saying he changed the expression in the equation at 7:02. I was like "what?".
I think that would be much easier method to solve that question if we are not confident with this Amazing teacher method:
E.g 2x²+7x-4=0
You multiply the coefficient with -4 = -8
x²+7x-8=0
(X-1) (X+8)=0 and you divide by the Coefficient;
X= -1/2 and X= 8/2 and you change the signs,
Finally, we could end up getting the same answer which is,
X=1/2 or X=- 4.
So that’s how you do it! Can’t believe I got passed 6th grade, my high school math teacher sent me here lol.
Recently, I was shown the "box and diamond" method. Look for it. WAY easier. You get the answer in fewer steps, with fewer fraction.
Make a "box" - a rectangle with four areas, and a diamond - a big X with four areas
Fill in the upper left of the box with ax^2 (in general terms) which is 2x^2 here.
Fill in the lower left of the box with c (in general terms) which is -4 here.
Fill in the top of the diamond/X with the product of those two terms, acx^2 = -8x^2 here
Fill in the lower part of the diamond/X with bx = 7x here
That's all rather close to automatic. You do have to multiply ax^2 times c.
Now you have to think a bit. What two terms multiply up to acx^2 and add down to bx. It's not really up or down, but that's how the diamond/X looks. You want the factors which add to the middle term. You've done that before, it just looks different now and you can handle a non-zero coefficient to the x^2 term easily.
When you find your answers, fill in the diamond/X and then the box.
Now find the common factors for each row on the box, write them outside. This is harder to describe in words than it is to see in a drawing. For my box, I have 2x^2 on the top and added the term 8x and then on the bottom row I have added the term -x and I have -4.
The factor across the top is 2x (goes into both 2x^2 and 8x) and across the bottom is -1 (goes into -x and -4).
The factor of the first column is x (goes into 2x^2 and -x).
The factor of the second column is 4 (goes into 8x and -4).
Just as Brian does, you can easily re-check by multiplying.
Then group the factors. On the left of the box are (2x-1) and across the top are (x+4). Set each equal to 0 and solve.
Really. I know it's a lot of words, but it's so easy!
bro overcomplicated it, took me 4 lines
a quick tip for people who use a lot the quadratic formula:
check if a+b+c=0. if so the 2 solutions are:
x=1 or x= c/a
Sir: I'm no mathma-wiz here. Can you give an example where one can use these equations in everyday situations? Thanks
I'm no math wiz either, but I think the idea behind all this is, you'll never know what it will apply to in the future. A lot of the math we use to create computers and algorithms is from math discovered a few hundred years ago. Can you use this in an everyday situation? Probably not. Can some person smarter than us use this math to create a future technology that we can't comprehend? The chance is not zero. I'm not trying to be a smart ass or anything, but I've always been fascinated by the idea that a really genius person can create something so useful with something that rest of us find useless.
@@ninjaguysith Thanks much, your last sentence make sense now, no one else has ever been able to explain or shed any light on rationale for these equations. Thanks again.
You "use" equations like this every day. Extend the complexity a couple of steps, move it to three dimensions, and that's how your GPS receiver calculates your location.
@@briant7265 Excellent, thanks
Sir, you are making this too complicated. There's a much easier way of solving this problem.
Alternative way: 2x² + 7x - 4 = 0 so a = 2 b = 7 c = - 4
Now we divide a = 2 by itself so 2/2 =1 and c multiplied by a so - 4 . 2 = - 8 and we get
2/(2) . x² + 7 . x - 4 . (2) = 0 or x² + 7x - 8 = 0
Easy to factorise in (x + 8) . (x - 1) = 0 and then we multiply the x with the original value for a so a = 2
(2x + 8) . (2x - 1) = 0 2x + 8 = 0 -> x = - 4 and 2x - 1 = 0 -> x = 1/2
And of course there is the abc-formula x1 , x2 = xtop -/+ delta like x1 .. delta .. xtop .. delta .. x2
Discriminator D = b² -4ac (0, 1 or 2 solutions for y = 0 when negative, zero or positve)
Symmetry axis of the parabola: xtop = - b / 2a
Distance between x1 , x2 and xtop: delta = V(D) / 2a
When you are asked to solve a quadratic equation by completing the square these alternative ways are easy to check the answer.
This vid helped a lot, I don't think I ever knew how to complete the square when the coefficient of a quadratic equation was greater than 1
great! now you know!
You can just use the quadratic formula
@@brianmclogan great videos
Thank you Mr. McLogan you are doing an excellent job I have improved tremendously in Algebra.
watching this in preparation for a test I"ve got to take over zoom tomorrow. Made me so sad :/ kinda miss being in a real classroom
same
how was the test?
OMG that's the exact same reason I'm here today 😭
You created so much more work and confusion right from the start by factoring out a 2 from the left side only, instead of dividing all terms by 2. Way to make it more complicated "teacher".
You lost me after placing the square. But I learnt a new skill before I got lost.
Thanks, I've been really struggling on completing the square and solving quadratic equations overall. Your video helped clarify step by step in the littlest detail. Once again, thanks man.
Use the expression: (-b +/- V(b2 -4.a.c) / 2a , and it will be done, haha
Haha, almost as if we need to know how to derive the formula by completing the square
YES! But he's teaching ANOTHER METHOD of solving it. So now you have 2 ways to solve it.
You made it so complicated. First divide both sides by 2 then find perfect square easily by adding and substracting the same amount b^2
Bao Le that’s right this is the hard way
Any sensible person would split the middle term
you are a life saver Mr. McLogan
IF YOUR SCROLLING THRU THE COMMENTS DONTT WATCH THIS ! His way of teaching drivers me maddd
Thanks Hanan, I have a ton of other examples
Good teacher I love mathematics
Thank you this is really helpful! It would be great if you could upload some problem solving questions that include completing the square or parabolas in general. Thanks
I just made some videos on that, will be uploaded within the next week. If you need some examples now, here is just one of my playlists with completing the square th-cam.com/play/PL0G-Nd0V5ZMq-1D6604jY8aFUjYuk4Kkh.html
Can you divide all the terms by 2 and then continue solving the problem?
in my head i revert back to a FOIL method and solve each for 0. giving me 1/2 and -4, proofed it and all under 2 minutes. not bad for an older guy that hasn't seen a quadratic for 26 yrs. (actually i'm just glad I had the right answer LOL)
Beaucoup trop long alors qu avec le discriminant il faut 10 secondes mentalement
glad he walked all the steps through and described where what came from to get to.
Hi, thanks for this video really helped! I was just wondering how you could find the turning point from this?
you would need to find the vertex. when you convert the equation to vertex form the vertex is (h,k) I have plenty of videos on finding the vertex by completing the square
ok thanks will have a look
"how you could find the turning point from this?"
1) Easiest when the coefficient of x is an even number eg (from my reply above):
eg with y = x^2 -4x -2 , completing the square yields
y = (x -2)^2 - 6 . Now look at the (x - 2)^2 , which has a minimum value of 0, when x = 2.
So the quadratic has a minimum value of -6 when x = 2.
The Vertex is the point (2, -6), which also reveals the Axis of symmetry ie the line x = 2.
OR
2) From y = ax2 + bx + c, calculate -b / 2a. This is the x-coordinate of the vertex.
To find the y-coordinate of the vertex, substitute the value of x = -b / 2a into the equation for x and solve for y.
OR
3) Find dy/dx, which = 0 at the turning point (Vertex)
From y = x^2 - 4x - 2
dy/dx = 2x - 4 which = 0 when x = 2 (substitute back into y, and y = -6)
Which method you'll use will beceome clearer to you with practice.
Thanks Mr Brian McMathman!
i love how he acts that he has students in the room or is he?
I think he just records his actual classes
are you okay?
Actually he has.
I did it in 30 seconds:
2x^2 +7x - 4 = 0
1/ delta=b^2 - 4ac = 81 ,
2/ sqr delta =9 ,
3/ X1= 4 , x2 = -1/2
Eot
I'm actually in love with this man.
Thanks!
Mr.McLogan you are such an amazing teacher, my math teacher is literally not teaching us properly, thank you so much ☺️
x1,2= (-b+-sqrt(D)) / 2a....where D= b^2-4ac... equation solved in 30sec. 4 years after leaving school and no contact with math
Wow! A simpler way, a*c = 2 * -4 = -8, b = a + c = -7. pair up, the factors are -8 and 1 => apply ax and the factors then simplify => (ax + factor 1)(ax + factor 2) => (2x - 8)(2x + 1) -> 2(x - 4)(2x + 1) => get rid off common factor 2 => (x - 4)(2x + 1) => x =4 or 2x = -1 -> x =4 or x = -1/2
Missed the important step of checking that your answer actually works.
I did that.
Thank you very much Mister McLogan.
Thanks so much! For some reason I had no idea that I had to multiply the factored out number with the 'c' variable.
You are very welcome
Thank you so much this was so helpful ☺️
This is going to help me so much in tomorrow's exam! Thanks from the UK!
cheers! good luck
Thank you for these videos teacher, mostly I watch only your videos :) thank you for being my virtual teacher!!
Yeah thats too many steps ill just get a 0 for this assignment 💀
This is a long way of approaching the problem, I have other videos more quickly
right☠️this is too much for one problem
I’m on this level of math, I just needed too figure out the answer and all of sudden you added additional info to it.. got confused need to watch it again I guess.. to understand.. appreciate the help..