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@@xsageonexx7399 Take, for example; x + b Square it: (x + b)(x + b), and carry out the multiplication to get the product: x^2 + 2bx + b^2 In the example polynomial, the 7/6 coefficient is your 2b, so you need to divide by 2, or multiply by 1/2 to get the value of b to add to the L-value to produce a perfect square.
I'm French. I'm retired (after a professional career in data processing). I love mathematics (it doesn't mean I'm an expert of it :-) and I APPRECIATE A LOT your videos. Thanks to them we can approach a high level of problem resolutions as this one in which the irrational number i is used to get the solution. Congratulation and thank you for sharing with us your high level knowledge.
6x^2-7x+8 =0, a= 6, b = -7, c = 8, -b = 7, b^2 = 49, 4ac = 4×6×8 = 192, b^2 -4ac = 48-192 = - 144 < 0 Since it is negative , this equation has no real roots.
For me it is very funny how you calculate the right side of the equation. You could do it like this: -4/3 + 49/144 = -192/144 + 49/144 = -143/144. Your way to do it seems like if a mountain hiker wants to reach the height of 1000 meters, so he goes up to 5000 meters and then comes down.
Or, in order to keep everything in integers for as long as possible, note that the middle coefficient is odd, so multiply by 4·6 (rather than by 6): 4·6·6x² - 24·7x = -24·8 12²x² - 2·12·7x = -192 12²x² - 2·12·7x + 7² = 49 - 192 (12x - 7)² = -143 x = (7 ± i√143)/12 Fred
Dumb question maybe but half of 2nd coefficient is 84, so don’t follow how you’re getting to 7squared instead of 84squared? Trying to relearn basic math to help my kids :). Thx.
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Excellent presentation. Thank you for this. I am now clarified that in finding a certain number to complete a square, we can possibly arrived on an imaginary number (ì). Kudos! Well explained.
You're very welcome Danny! Thank you so much for taking the time to leave this comment. I'm glad you liked it! Your feedback is always appreciated. Please keep supporting my channel. Kind regards :)
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You are very welcome Oordnajela Zitro ! Thank you so much for taking the time to leave this comment. I'm glad you liked it! Your feedback is always appreciated. Please keep sharing my channel with your family and friends.Take care dear and all the best😃
This is so relaxing to the brain I feel loads just got lifted off my shoulders. I love getting a refresher on this; thanks very much for the link. It's been at least two years since I last did these equations.
In germany we have something that's called pq-Formel: when you see this equation x^2 + qx + q = 0, you can do this: X = - p/2 +/- Squarerootof [ (p/2)^2 - q]
@@BigWailz_official the solutions to ax^2 + bx + c = (-b +/- sqrt(b^2 - 4ac))/ 2a. This seems quite complicated, but once you use it a couple of times, you find that unless factorisation is very simple, it's the simplest method, and I always find it simpler than completing the square. It works all the time and you can also tell very simply how many real solutions there are based on whether the value in the square root is positive (2), zero (1) or negative (0).
Andy Wright that might be so, but the whole point of the video was to show that the completing the square method could be used - as his student had asked him. It does also bring in the concept of the imaginary number rather nicely and also builds on knowledge of splitting number to root them which is convenient too, for building in and reinforcing concepts covered in earlier lessons.
So nice of you Bisma dear! You are awesome 👍 I'm glad you liked it! Please keep sharing premath channel with your family and friends. Take care dear and stay blessed😃
@ around 4:10 you put (7/12)^2 On both sides. later you said what sign to put in between x and 7/12 whole square... It wasnt necessary...you simply should have said...its taking on the form of a^2 - 2ab+b^2. And will so...reduce to (a-b) ^ 2 .That way it would have been simpler....
Completing the square for this expression would be much better than beginning with the equation, as this also derives the coordinates for the vertex. If only roots are needed, then the formula is the obvious choice. Moreover, you should review adding fractions. -4/3 + 7^2/12^2 = -43/12^2. Only beauty lies in true mathematics.
Can you bring the answer all over 12 (because of common denominators) or does the inclusion of 'i' not make that possible? (7 + i(143)² ) / 12 and (7 - i(143)² ) / 12 .
Wonderful! Can we always take the half of coefficient number by 1\2...? And also can we also directly write the number obtained when multiplied by the coefficient number without making it smaller?
I’m long out of math. Like these videos to refresh my mind. What is the purpose of completing the square? Knowing the formula I would never bother with this. Is their a reason to?
Thanks sir This is my dad's phone .My teacher taught me this 5 five but i was not understanding .but yoday i saw ur video , u are fabulous I understood very fast
You're very welcome Umesh! Thank you so much for taking the time to leave this comment. I'm glad you liked it! Your feedback is always appreciated. Please keep supporting my channel. Take care dear 😃
May I suggest that when you combined the fractions, it would have been preferable to use the lowest common denominator, 144, rather than cross-multiplying, as this would lead to easier arithmetic with smaller numbers and avoid the need to cancel by sqrt(3) later.
Love the You Tube name you use. Reminds me of one of my favorite Adages. "Math is a Wonderful Thing. Become good enough at it, and no one will EVER be able to fool you with demagoguery." As for this video, my 8th grade algebra teacher took us through a drill very similar to this one. I raised my hand and asked "Wouldn't it be easier to just apply the Quadratic Equation?" He replied "With an attitude like that, you'd be better off becoming an Accountant than a Mathematician." So I did LOL All best!
I knew immediately that they were imaginary because the nature of the root (or the discriminatnt I.e. b^(2)-4ac) is less than zero so it must mean it has two imaginary solutions. Great video👍👍
Thanks Safeer for the comment. I've visited your channel as well. You are very talented and inspiring teacher. Therefore, I've gladly subscribeddd your channel as well. I upload my videos every day. Please don't forget to comment and LIKE on my videos. I wish you all the best. Keep it up.
My daughter is using this mathematics to solve her assignment
Thanks for your help and support.
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Good . But what Is the meaning of each step . Why we add the steps that we wanted , there should be some meaning right
Plz watch
m.th-cam.com/users/Niteshsir
@@PreMath Why do you:
A. Pull the 7/6 aside and
B. Divide it by 2?
@@xsageonexx7399 Take, for example; x + b
Square it: (x + b)(x + b), and carry out the multiplication to get the product:
x^2 + 2bx + b^2
In the example polynomial, the 7/6 coefficient is your 2b, so you need to divide by 2, or multiply by 1/2 to get the value of b to add to the L-value to produce a perfect square.
I'm French. I'm retired (after a professional career in data processing). I love mathematics (it doesn't mean I'm an expert of it :-) and I APPRECIATE A LOT your videos. Thanks to them we can approach a high level of problem resolutions as this one in which the irrational number i is used to get the solution. Congratulation and thank you for sharing with us your high level knowledge.
9:16 When used as an operator, ± should be spoken as "plus or minus".
"positive or negative" is correct only when ± is used as a sign.
Yeah, contexts. Our teacher from math would note that, just like in your comment.
6x^2-7x+8 =0,
a= 6, b = -7, c = 8,
-b = 7,
b^2 = 49,
4ac = 4×6×8 = 192,
b^2 -4ac = 48-192 = - 144 < 0
Since it is negative , this equation has no real roots.
Именно так, и квадрат числа не может быть отрицательным, какой же тупой автор видео
For me it is very funny how you calculate the right side of the equation. You could do it like this: -4/3 + 49/144 = -192/144 + 49/144 = -143/144.
Your way to do it seems like if a mountain hiker wants to reach the height of 1000 meters, so he goes up to 5000 meters and then comes down.
Same thoughts! I'm really bothered with how he added the fractions 😂
Exactly.....
Good professor 🌷💐🌺🌺💐
Thanks and welcome
You explain very well👍
Or, in order to keep everything in integers for as long as possible, note that the middle coefficient is odd, so multiply by 4·6 (rather than by 6):
4·6·6x² - 24·7x = -24·8
12²x² - 2·12·7x = -192
12²x² - 2·12·7x + 7² = 49 - 192
(12x - 7)² = -143
x = (7 ± i√143)/12
Fred
0
ffggddss :thanks so much sir,your explanation is so clear
Genius
Now i got the point of denoting quadratic root of negative numbers. Thank you.
Dumb question maybe but half of 2nd coefficient is 84, so don’t follow how you’re getting to 7squared instead of 84squared? Trying to relearn basic math to help my kids :). Thx.
Please make a video on real life use of limits , mathematical induction,complex numbers
So best and great video but l am daily using video wow amazing sir l like you video
1:28 "The next thing what we want to do" ... I'm so glad this isn't an English lesson ... "isn't it".
Amazing Good
Well done
Thank u sir
Step by step approach to answer is simply super.
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Good explication. Thanks
Excellent presentation. Thank you for this. I am now clarified that in finding a certain number to complete a square, we can possibly arrived on an imaginary number (ì). Kudos! Well explained.
You're very welcome Danny! Thank you so much for taking the time to leave this comment. I'm glad you liked it! Your feedback is always appreciated. Please keep supporting my channel. Kind regards :)
Very well explained! Would using the quadratic formula result in the same answers?
Thank you so much I was able to challenge some people
Thank you so much for your explanation. I'm from India 🇮🇳but I can understand your explanation comletely.👍
You are very welcome Patel ji! Thank you so much for taking the time to leave this comment. I'm glad you liked it! Your feedback is always appreciated. Please keep sharing my channel with your family and friends. Take care dear and all the best😃
presente, nuevo por aquí, que gran canal, felicitaciones
This is to help me refreshing for my daughter’s pre calculus . Thank you very much !!!!
Very clear to me as a student... Tnx
You are very welcome Oordnajela Zitro ! Thank you so much for taking the time to leave this comment. I'm glad you liked it! Your feedback is always appreciated. Please keep sharing my channel with your family and friends.Take care dear and all the best😃
Thank you for all this great knowledge
This is so relaxing to the brain I feel loads just got lifted off my shoulders. I love getting a refresher on this; thanks very much for the link. It's been at least two years since I last did these equations.
Can you explain pls how and why are you dividing 7/6 by 2...where did you get that 2
Anyone teaching equation should explain the rules........ Whenever someone understands the rules, everything becomes easy.
The rules?
Pure bs dreamt up by some arab this shit is out dated
Pretty good sir! Best explainer
Thanks dear for the visit! You are awesome 👍 Take care dear and stay blessed😃 Kind regards
Very very good
Very nice
Super super
In germany we have something that's called pq-Formel: when you see this equation x^2 + qx + q = 0, you can do this: X = - p/2 +/- Squarerootof [ (p/2)^2 - q]
Good thanks
Thank you too!
Solving with the equation is much simpler
A=6, b=-7, c=8
X=(7+/-sqrt(49-4×6×8))/12
=(7+/-sqrt(49-192))/12
=7+/-sqrt(-143))/12
=7/12+/-sqrt(143)i/12
Thank you. This is correct
Please can you break down the simplification process so I can understand
@@BigWailz_official the solutions to ax^2 + bx + c = (-b +/- sqrt(b^2 - 4ac))/ 2a. This seems quite complicated, but once you use it a couple of times, you find that unless factorisation is very simple, it's the simplest method, and I always find it simpler than completing the square. It works all the time and you can also tell very simply how many real solutions there are based on whether the value in the square root is positive (2), zero (1) or negative (0).
Andy Wright that might be so, but the whole point of the video was to show that the completing the square method could be used - as his student had asked him.
It does also bring in the concept of the imaginary number rather nicely and also builds on knowledge of splitting number to root them which is convenient too, for building in and reinforcing concepts covered in earlier lessons.
We can ×6# 36 x^2_42x+48=0 then (6x_7/2)^2=_47/2
Very good presentation
Thanks a lot :)
Diff method also solve
Content - can you solve this
Me - No, that's why I am going to see this video
Legends - No, and I don't need to 🤣
That's the method every student should master. Thanks.
Just subscribed ! You are a life saver
So nice of you Bisma dear! You are awesome 👍 I'm glad you liked it! Please keep sharing premath channel with your family and friends. Take care dear and stay blessed😃
I liked and watched the video!!
Great work done
Good
You kan simply solve it with
(X= -b + and - √b squar - 4ac all over 2a, a as 6 ,b as -7 ,c as 8
Mustafa Sleiman that’s not fun
That’s not what his student asked him to do.
Really appreciate it sir👌
Thank you.... thank you soooo very much sir......I was facing prblm in this thing for many days....
Thanks for clearing my doubt.........😊
Why to fill c ( notation a, b and c) was b divided 2, where was 2 come from?
Thanks sir I gree with you
Thank you.
You're welcome!
@ around 4:10 you put (7/12)^2 On both sides. later you said what sign to put in between x and 7/12 whole square...
It wasnt necessary...you simply should have said...its taking on the form of a^2 - 2ab+b^2. And will so...reduce to (a-b) ^ 2 .That way it would have been simpler....
Explanation was very good. You please shutup
You are correct.
Why did you divide 7/6 by 2? Please clarify.
Completing the square for this expression would be much better than beginning with the equation, as this also derives the coordinates for the vertex. If only roots are needed, then the formula is the obvious choice. Moreover, you should review adding fractions. -4/3 + 7^2/12^2 = -43/12^2. Only beauty lies in true mathematics.
Thanks dear for the nice feedback. I really appreciate that.
Take care dear and all the best😃
Have a very happy and blessed New Year!
Well done sir but you made it long instead of short
You cannot take Square root of an expression. It has to be in simplified form. Else it should be in Modulus.
If ax2+bx+c =0, the solution of formula is -b+-✓ b2-4ac（radical symbol)/2a.
Exactly right
3 is a factor of 144. You only needed to multiply -4/3 by 48/48 and then add with 144 denominator. You could have saved steps there
Can you bring the answer all over 12 (because of common denominators) or does the inclusion of 'i' not make that possible? (7 + i(143)² ) / 12 and (7 - i(143)² ) / 12 .
Wonderful! Can we always take the half of coefficient number by 1\2...? And also can we also directly write the number obtained when multiplied by the coefficient number without making it smaller?
I mean can we always multiply the coefficient number by 1\2
Pleas solve the 18x² + 3x - 15
Great sir.Thank you so much👍👏
Thank you so much
I’m long out of math. Like these videos to refresh my mind.
What is the purpose of completing the square? Knowing the formula I would never bother with this. Is their a reason to?
hahaahahahahahaha great question. well i guess teachers want us to fail, thats why
it can help with maximums
Thanks sir This is my dad's phone .My teacher taught me this 5 five but i was not understanding .but yoday i saw ur video , u are fabulous I understood very fast
You're very welcome Umesh! Thank you so much for taking the time to leave this comment. I'm glad you liked it! Your feedback is always appreciated. Please keep supporting my channel. Take care dear 😃
question. Why do u need to flip over the 2 over 1?
Subscribed! Great explanation!
Thank you so much! Please keep supporting my channel. Kind regards 😀
Sir how to solve this equation by factorization
Hi. What lecture app and/or tablet did you use in your online lecture? Thanks.
Very helpful
need more explanation because why should we take square of 7/2. There is logic behind and this logic should be explain. good effort
L.C.M.of 3 and 144 is 144 so -4x48+ 49 gives -143/144
X=1.876,-0.71 answer sharing, thanks sir,is it correct?
What happened to the -7/6x?
Thanks you sir for this video i got 5/5in my test of this topic thank you soo much ❤❤❤❤
Most welcome 😊
@@PreMath why in 2:20 you had to divide by 2/1
very good explanation... you are really good teacher and not for duffers like some of those who commented below....
Thank u so much sir
In electronic engineering, " i " is replaced with " j ". The reason for that is, lower case " i " is the current symbol in AC circuits.
Great work
#LearnMathwithZain
AWESOME THANK U FOR YOUR HELP💔
X=squareroot of 7x-4 OVER 3
@5:39 in video (-429/432) reduces to -(143/144)
johnnie gilkerson hahaha, exactly
Please help me why did he put 3.143 and 3.144 @ 7:40
You are excellent ,that is the way I learned by doing all the steps.
Really - b+-root over b square - 4@c / 2a simple why to do this much and gone to pit of gutter
Sankalp Nagar because they have to do it that way
Nice video!
What is the name of boared please ??
Divide:(12x^4-15x^3)÷3x^2 please
May I suggest that when you combined the fractions, it would have been preferable to use the lowest common denominator, 144, rather than cross-multiplying, as this would lead to easier arithmetic with smaller numbers and avoid the need to cancel by sqrt(3) later.
Can we multiply and divide the coefficient of x by 2 ?
I know this method and this method is given in book examples
Thats what people dnt understand. Actually i ve to use that method for my hw.
Wow lam sure acsayte 👌👌👌👌👌🇮🇳🤗
Really usefull class.
144 and 3 have a lower common multiple 144
Great video. As a math teacher myself, I love how you skipped no steps.
MathGives YouPower , thanks for the honest feedback. We both are in this very noble teaching profession. Kind regards :)
Love the You Tube name you use. Reminds me of one of my favorite Adages. "Math is a Wonderful Thing. Become good enough at it, and no one will EVER be able to fool you with demagoguery."
As for this video, my 8th grade algebra teacher took us through a drill very similar to this one. I raised my hand and asked "Wouldn't it be easier to just apply the Quadratic Equation?" He replied "With an attitude like that, you'd be better off becoming an Accountant than a Mathematician." So I did LOL
All best!
where did the 7/12 and 2/1 come from? I think I have frozen my brain. I love math; this has me stumped. I would make my dad, the math prof so proud :)
It can be solved by using Middle Term Spilitting also
I knew immediately that they were imaginary because the nature of the root (or the discriminatnt I.e. b^(2)-4ac) is less than zero so it must mean it has two imaginary solutions. Great video👍👍
hahaha who cares fucking knowitall hahaha
Gauss.
lol
luis portella You can’t comprehend such low level math? Hahaha.
Nice sir
Thanks Safeer for the comment. I've visited your channel as well. You are very talented and inspiring teacher. Therefore, I've gladly subscribeddd your channel as well. I upload my videos every day. Please don't forget to comment and LIKE on my videos. I wish you all the best. Keep it up.
144&3 lcm 144
with i²=-1 it is wunderfull
I watched and liked it
please how to creat a matematics videos
Dear Hassan, I use CamtasiaTechSmith utility for my videos. Take care😃
@@PreMath Thank you so much
@@profbenchahyd8776 My pleasure 😃
Why you use xsquare coefficient is one
Just solve for x to the first power and iteratively solve.
Thanks Boss
Why don't you keep the captions what you talk on one side so that the steps by steps solution is not hidden.?
Same answer with the quadratic formula
If you want to make surface spread there are two solutions for I. An upper curve and a lower one.