I am a 11th student (in India high school is 11th and 12th), wasn't able to understand this method from past 5-6 months, but this 1 video did something that no other teacher did in such a long time. thnx
You really are an engaging math teacher, and certainly dont fit the stereotype of a math teacher!!! Your youtube videos are so much more intresting than my coaching classes or school. Please, do keep doing what you are doing, for atleast I, for one am really grateful. And i am sure there are many. Thanks a lot, sir.
@@TYCuber You can watch this really amazing video to learn how to. It's a bit long but you can learn a lot. There you go -> th-cam.com/video/MHXO86wKeDY/w-d-xo.html
It seems such a tragedy that someone’s ability to understand something - and it doesn’t have to be mathematics - can come down to the lottery of who teaches them. Something else that baffles me, is why there is such variation in teaching ability. This guy is clearly off the scale, at the other end was my history teacher, who sat at his desk reading from the text book - word for word - and we wrote down what he said - and that was every history lesson we had with him for two years!
Brings up "perfect square" - 2:42 Explains and demonstrates at six:13 of _Completing the Square (1 of 2: How does it help?)_ Very simple, but with so many new concepts at once some can get lost
Mr. Woo you said at 5:55 "all quadratics all of these guys they all end up with tow solutions don't they" , what if the quadratic is x^2 -10x + 25 =0. Then X would be 5 only, which is only one solution. Is this a special case or does it still have two solutions like 5 + 0, 5 - 0 etc?
ok I found my answer to my own question on your other posted video. Quadratic Functions: What the Discrimant tells you . 4:00 th-cam.com/video/dZs9tIVnQvk/w-d-xo.html One Double root or Two Equal roots. Keep up the good work. Eddie Woo. I love maths when I was 14 your videos has respark the same love now that I am 55.
1:35 - Should this work with the answer derived at 8:04 ? He says "like you predicted" But the prediction (as I see it) is multiplication And his method ultimately used addition 8:04
okay I've figured it out. He shows the roots as if they are the factors. The factors to be made equal to zero would be (x + 3 - sqrt(2)) and (x + 3 + sqrt(2)) so 3 - sqrt(2) + 3 + sqrt(2) = 6 and 3 - sqrt(2) * 3 + sqrt(2) = 7
It's not necessarily a literal square in geometry. It is more of an application of squaring numbers in general. The namesake of squaring numbers comes from the area of squares in geometry, but there are applications all over math and science where squaring numbers has nothing to do with actual squares where you can measure both sides with a ruler. It only relates to actual squares on a graph of the variables involved. I'll give you an example. The energy stored in a deformed spring is given by the equation E=1/2*k*x^2, where k is the stiffness constant, and x is the distance it is stretched from its relaxed position (where x is defined as zero). The reason why 1/2 is in this equation isn't important for my main point, but I'll be willing to address this question if you'd like to know. If you've ever played with a spring, you know that some springs can be both stretched and compressed, depending on how they connect at the ends, and as long as it has the right geometry to not buckle. There is symmetry to a spring's behavior in compression, to its behavior in tension, just like there is symmetry in the equation of y=x^2. The spring applies a force that is proportional to, and opposite, the deformation from its neutral state. When the spring is compressed, x is a negative number by convention. Since there is energy stored in a spring, both when stretched 3 cm, and when compressed 3 cm, we can square either 3 cm or -3cm, and end up with the same energy stored in the spring, in both modes of loading. The energy stored in the spring is proportional to the "area" of the square of the deformation of the spring. For tension, it makes sense for the 3cm deformation to correspond to the side of a 3x3 square that is 9cm^2 in area. But for the compression case, no literal square is -3cm by -3cm. Yet energy stored in the spring is still proportional to the same 9cm^2 in area, that the -3 cm x -3 cm square would have.
Denzel curry the goat Because they haven’t learned it yet. This is usually taught right before you learn the quadratic formula, because this method is how you derive the quadratic formula.
@@wsk5nwytscnkfsu Well we haven't proved it yet. I'm proving it myself and I don't like the proof by completing the square. Makes sense but it's wierd. I'm proving it by graphing (If you're interested on what I've done see below) So I have ax^2 + bx + c = 0 Now notice how the turning point of a quadratic it's slope is flat (0). So derive the function and we get 2ax + b = 0. And this is a line that crosses the x axis right above the quadratic. We now find the x value which is -b/2a . That is the center of our quadratic. Now we have a distance with some form of "d". There is positive d and negative d (root to the right of our center, root to the left of our center) Root->\ - -b/2a. + /
Himanshu Padnani. Yes I am aware that the quadratic formula is derived from completing the square, but that's not what I asked. What I am trying to get at here is , why isn't this question asked, why would you need to complete the square? What are the advantages over using the formula? Showing someone how to complete the square without explaining the ' why you would need ' to do it is rather pointless. It becomes analogous to teaching someone calculus, by various methods of integration and differentiation without explaining the concept of the 'limit' from which it is derived. Don't get me wrong here, I appreciate your reply and thank you for it. I personally find that quite a lot of mathematical concepts and ideas become difficult to understand if not explicitly explained and derived from first principles, what's the point in learning by rote? There's those who know what they teach and those who can teach what they know, and they are as different as chalk and cheese. Peace to you and respect.
Barry Hughes It's not very intuitive, people don't just intuitively use the formula if they are not exposed to it. It's faster yes, but the core understanding behind these elegant ideas is lacking.
Barry Hughes Because you can always forget or misremember a formula. But you will remember the method used to derive it. And you will be able to derive the formula whenever you forget.
As you probably know, completing the square has one advantage over the formula. Its format reveals the coordinate of the turning point of the curve in a very visual way.
Awesome Video! But I don't agree about the comment you made in 0:52. It's not trial and error method, you should never teach that mate. In this video, th-cam.com/video/MHXO86wKeDY/w-d-xo.html , 3b1b explained the same method (splitting the middle term) but without using the trial and error method but using maths. He actually solved the same example you chose to make the students understand that splitting the middle term method is not good enough.
i know im 6 years late but you did not explain th epart of completing the square where you have to divide b by 2 and square it, thats how you got 9. you just gave the kids another problem without fully explaining the first one. wow
Sneaky with that multiplication of your solutions! You are supposed to switch their signs, which makes no difference with multiplication, but eagle-eyed students may have noticed when you add your solutions as is, the sum is -6 instead of 6.
Holobrine We got the value of X (i.e) -3-√2 or -3+√2 If you want check whether it is correct or not then substitute the value of in the starting equation i.e X^2+6X+7=0. Why are you adding those values??
ax^2 +bx + c = 0, then sum and product of roots of the Quadratic equation are -b/a and c/a respectively. And you can easily see that the sum and product of roots is - 6 and 7 accordingly. So solutions are correct.
I am a 11th student (in India high school is 11th and 12th), wasn't able to understand this method from past 5-6 months, but this 1 video did something that no other teacher did in such a long time. thnx
You really are an engaging math teacher, and certainly dont fit the stereotype of a math teacher!!! Your youtube videos are so much more intresting than my coaching classes or school. Please, do keep doing what you are doing, for atleast I, for one am really grateful. And i am sure there are many.
Thanks a lot, sir.
Shalersa Sandre I would like this but it’s sitting on 69
I would like it and I did :)
"the stereotype of a math teacher", lmao. the girl tried to be kind but failed
This is a much better explanation to what I got in highschool. Great Job
+Daniel Brown Yeh he is the best
he is our head maths teacher and the best in my eyes
1:56 "But 1 and 7, at least last I checked, 1 and 7 do not add up to 6"
Good point
You know, you can solve that equation with that method, he just didn't wanted to.
@@Crucizer no you can’t
@@TYCuber You can watch this really amazing video to learn how to. It's a bit long but you can learn a lot. There you go -> th-cam.com/video/MHXO86wKeDY/w-d-xo.html
@@TYCuber You can, but not with whole numbers.
@@TYCuber you can do 7 and -1
man like eddie promising he won't spoil the subheading when he spoilded the seubheading in the video title
man like
It seems such a tragedy that someone’s ability to understand something - and it doesn’t have to be mathematics - can come down to the lottery of who teaches them. Something else that baffles me, is why there is such variation in teaching ability. This guy is clearly off the scale, at the other end was my history teacher, who sat at his desk reading from the text book - word for word - and we wrote down what he said - and that was every history lesson we had with him for two years!
You are by far the best teacher I’ve ever seen teach it’s honestly incredible
Brings up "perfect square" - 2:42
Explains and demonstrates at six:13 of _Completing the Square (1 of 2: How does it help?)_
Very simple, but with so many new concepts at once some can get lost
I have a quiz on this, Friday and this helped so much. Thank you
Mr. Woo you said at 5:55 "all quadratics all of these guys they all end up with tow solutions don't they" , what if the quadratic is x^2 -10x + 25 =0. Then X would be 5 only, which is only one solution. Is this a special case or does it still have two solutions like 5 + 0, 5 - 0 etc?
ok I found my answer to my own question on your other posted video. Quadratic Functions: What the Discrimant tells you . 4:00 th-cam.com/video/dZs9tIVnQvk/w-d-xo.html
One Double root or Two Equal roots. Keep up the good work. Eddie Woo. I love maths when I was 14 your videos has respark the same love now that I am 55.
1:35 - Should this work with the answer derived at 8:04 ?
He says "like you predicted"
But the prediction (as I see it) is multiplication
And his method ultimately used addition 8:04
tysm mate, you got me through math
7:05 He says that those two numbers will give the results of _ + _ = 6, but
(-3 - sqrt(2)) + (-3+ sqrt(2)) doesn't equal 6. It equals -6.
okay I've figured it out. He shows the roots as if they are the factors. The factors to be made equal to zero would be (x + 3 - sqrt(2)) and (x + 3 + sqrt(2))
so 3 - sqrt(2) + 3 + sqrt(2) = 6
and 3 - sqrt(2) * 3 + sqrt(2) = 7
Why did the two solutions multiply to 7?
??
The last number will always be multiplied
(x+2)(x-3) = x^2 - x -6
Therefore 7 is also multiplied
I wonder how come an area has a side (width or height) that is negative?
It's not necessarily a literal square in geometry. It is more of an application of squaring numbers in general.
The namesake of squaring numbers comes from the area of squares in geometry, but there are applications all over math and science where squaring numbers has nothing to do with actual squares where you can measure both sides with a ruler. It only relates to actual squares on a graph of the variables involved.
I'll give you an example. The energy stored in a deformed spring is given by the equation E=1/2*k*x^2, where k is the stiffness constant, and x is the distance it is stretched from its relaxed position (where x is defined as zero). The reason why 1/2 is in this equation isn't important for my main point, but I'll be willing to address this question if you'd like to know.
If you've ever played with a spring, you know that some springs can be both stretched and compressed, depending on how they connect at the ends, and as long as it has the right geometry to not buckle. There is symmetry to a spring's behavior in compression, to its behavior in tension, just like there is symmetry in the equation of y=x^2. The spring applies a force that is proportional to, and opposite, the deformation from its neutral state. When the spring is compressed, x is a negative number by convention. Since there is energy stored in a spring, both when stretched 3 cm, and when compressed 3 cm, we can square either 3 cm or -3cm, and end up with the same energy stored in the spring, in both modes of loading. The energy stored in the spring is proportional to the "area" of the square of the deformation of the spring.
For tension, it makes sense for the 3cm deformation to correspond to the side of a 3x3 square that is 9cm^2 in area. But for the compression case, no literal square is -3cm by -3cm. Yet energy stored in the spring is still proportional to the same 9cm^2 in area, that the -3 cm x -3 cm square would have.
So engaging and now i finallt understand this thanks so much!!! I'm having fun learning and its a weekend....
Legend Eddie
It’s done being USED!
Why u dont use quadratic formila?
Denzel curry the goat Because they haven’t learned it yet. This is usually taught right before you learn the quadratic formula, because this method is how you derive the quadratic formula.
@@wsk5nwytscnkfsu
Not in my school. We learn quadratic first
No Hackers
That’s interesting. How was the quadratic formula introduced (proved) to you if your class didn’t learn this method first?
@@wsk5nwytscnkfsu
Well we haven't proved it yet. I'm proving it myself and I don't like the proof by completing the square. Makes sense but it's wierd.
I'm proving it by graphing
(If you're interested on what I've done see below)
So I have ax^2 + bx + c = 0
Now notice how the turning point of a quadratic it's slope is flat (0). So derive the function and we get
2ax + b = 0. And this is a line that crosses the x axis right above the quadratic. We now find the x value which is -b/2a . That is the center of our quadratic. Now we have a distance with some form of "d". There is positive d and negative d (root to the right of our center, root to the left of our center)
Root->\ - -b/2a. + /
Quadratic formula is the shortcut of completing the square, they need to understand how to complete the square in order to learn quadratic formula.
if you could work for khan academy it would be great
No he is good but sal khan is also a really good teacher
Yes…it would then feel like what was being taught was interesting and exciting - almost magic - instead of a robot teaching for an exam outcome
Cherrybrook teacher wearing Castle Hill's tie?? :o
how come the root -3 - sqrt 2 and -3 + sqrt 2 add up didnt go to 6? It is -6 instead?
I would suggest you watch this video. It also from Eddie too. th-cam.com/video/fVmwyVLEXoU/w-d-xo.html
Because -3 +- sqrt(2) are the roots. Sum of roots add up to -b/a where we have the equation ax^2 + bx + c.
Why would not just use the quadratic formula?
Barry Hughes Good One,
P.S. The Quadratic formula you are talking about is derived from this very completing squares method...
Himanshu Padnani. Yes I am aware that the quadratic formula is derived from completing the square, but that's not what I asked. What I am trying to get at here is , why isn't this question asked, why would you need to complete the square? What are the advantages over using the formula? Showing someone how to complete the square without explaining the ' why you would need ' to do it is rather pointless. It becomes analogous to teaching someone calculus, by various methods of integration and differentiation without explaining the concept of the 'limit' from which it is derived. Don't get me wrong here, I appreciate your reply and thank you for it. I personally find that quite a lot of mathematical concepts and ideas become difficult to understand if not explicitly explained and derived from first principles, what's the point in learning by rote? There's those who know what they teach and those who can teach what they know, and they are as different as chalk and cheese. Peace to you and respect.
Barry Hughes It's not very intuitive, people don't just intuitively use the formula if they are not exposed to it. It's faster yes, but the core understanding behind these elegant ideas is lacking.
Barry Hughes Because you can always forget or misremember a formula. But you will remember the method used to derive it. And you will be able to derive the formula whenever you forget.
As you probably know, completing the square has one advantage over the formula. Its format reveals the coordinate of the turning point of the curve in a very visual way.
surely (x+7) (x-1) ???? for the quadratic at 2 min 13 secs ???
Awesome Video! But I don't agree about the comment you made in 0:52. It's not trial and error method, you should never teach that mate. In this video, th-cam.com/video/MHXO86wKeDY/w-d-xo.html , 3b1b explained
the same method (splitting the middle term) but without using the trial and error method but using maths. He actually solved the same example you chose to make the students understand that splitting the middle term method is not good enough.
Anyone know how to do completing square for xsquared + 8x
(x+4)^2 - 16
"1 and 7 do not add up to 6" WHAAAAAAT !!! this is incredible.
Yeah , that's can be add ( +7,-1).but, if you multiply you get -7 not +7 🤦
Thanks mr duff
I'm sorry, please, correct me if I am wrong, but, those roots do not add up to 6!
He forgot a minus sign over there. They add up to -6, which is (-b/a) of that equation
Shouldn't they add to 6 but they add to -6 instead.
But 7-1 gives you 6.
But they multiply to -7, not 7.
You areee thee best !!!😭💞💕💖i always get u
i know im 6 years late but you did not explain th epart of completing the square where you have to divide b by 2 and square it, thats how you got 9. you just gave the kids another problem without fully explaining the first one. wow
2nd video lol
Spoiler free lesson 😂
Sneaky with that multiplication of your solutions! You are supposed to switch their signs, which makes no difference with multiplication, but eagle-eyed students may have noticed when you add your solutions as is, the sum is -6 instead of 6.
Holobrine
We got the value of X (i.e) -3-√2 or -3+√2
If you want check whether it is correct or not then substitute the value of in the starting equation i.e X^2+6X+7=0.
Why are you adding those values??
ax^2 +bx + c = 0, then sum and product of roots of the Quadratic equation are
-b/a and c/a respectively. And you can easily see that the sum and product of roots is - 6 and 7 accordingly. So solutions are correct.
M8