*kids clap and yell "Yay Math"*
Hi
I was sitting on the... floor
My elevator is broken, so
Oh wait I think I can fix it, here
There, now it's working
*kids laugh*
I can do the stairs
It's funny when you mess it up
HA HA, I love the laughing
All right here we go!
x squared, this one is really fun!
This one is super fun
I like it
I really like it
Usually we solve by doing what for this?
(student: factoring)
Factoring, yeah
So let's look at it, can it be factored?
Let's try
(student: Wait, no you can't.)
So we got someone saying it can't be factored
So remember numbers that multiply to 18?
Right, what are they?
6 and 3, 9 and 2, 18 and 1
if we were to but 6 and 3 here could that make 10?
(students: no)
If we were to put 9 and 2 here could that make 10?
(students: no)
If we put 18 and 1, no
No, it has to multiply to make 18
So, it can't be factored
So we have to have a new way to solve this
and the method is called "completing the square"
Here is how it works
First of all, this number needs to be 
moved to the other side
The last number, the "c", if you will. 
Yes?
(student: You add 18 to both sides)
You add 18 to both sides, thank you
x squared minus 10x equals 18
We added 18 to both sides
Now this number remains open
We need to find this magical number,
what must this number be
so that it can be factored?
And I'm going to tell you
how to find this number
Remember we talked about a, b, and c?
What's "a" in this case?
The number in front of x²
(students: Oh, 1)
What's "b"?
(students: Negative 10)
Correct, it is -10
And what's "c"?
(students: -18)
Good, so the number here has to do with b, 
we're going to change b around.
The number we put here is...
(student: That's the formula; a, b, and c?)
Yes, the formula has a, b, and c in it
a = 1, b = -10, and c = -18
So this number here, you take b, and you halve it.
What's half of b?
(students: -5) correct.
So you take b and you halve it, 
that's this, b/2.
Take b and you halve it then you get -5
Then you take that number, -5,
and you square it
25, right
every time, this thing here, this number, 
will be (b/2)²
So, we take b, -10,
 divide it by 2, that's  -5
(-5)² is 25
so we add 25 now
(student: To both sides?)
What ever you do to one side
what must you do to the other?
(students: The same)
Add 25 to both sides
Question?
(student: What I don't get is
why would you halve the b? The -10?)
Why would you halve the -10 and square it?
(student: yeah)
Because it is the only number that we can add so that we can make something like this
Now this is factorable
Not only is it factorable, 
it's a perfect square factor
So we're going to talk about what this is.
First of all, what's 18 and 25 together?
(student: 43?) 43, good.
Now, this number here is always, 
are you gonna guess?
(student: is it going to be half of b?)
Yes, it's b/2
(same student: So that's -5?) yeah
This number here will always be b/2
So what's b/2?
(students: -5)
So this becomes x - 5
So this is x - 5,
here it comes
We're going to prove this now, don't worry.
x minus 5
In other words, this part here:
x² - 10x + 25
and this thing,
are exactly the same.
Let's prove that.
What is x - 5 times x - 5?
(students yell over each other: x² - 10x +25)
x² - 10x + 25, so this works, good.
Now, at this point, what do you do to both sides?
Maybe get rid of the square?
Square root both sides
(student: How did you get rid of the x?)
We don't get rid of the x, it's still here
(same student: No the other one)
This squared, we agreed,
that this is the same as the -10x
So this is x, what?
(student: it's x² -10) No, no, no
We square rooted both sides,
so we got x - 5 equals 
(student: 6.5)
We are going to leave it in square roots, 
and we're going to say "plus or minus √43"
I want you guys to get used to the idea
that whenever you take a square root,
you make it ± the square root
(student: but you never can have a negative root)
Right, square root can’t result in a negative number
but you’re allowed to have negative square roots
Is x by itself yet?
What do we do with both sides?
(students: Add 5)
Add 5, and we're done
(student: So is that the answer, 
the problem is just done?)
The problem is done, our answer is...
x = 5 ± √43
(student: wait, that's the answer?)
That's the answer
(another student: is there any way to make it easier?)
No, that's the only answer there is
Two answers: (x = 5 + √43) or (x = 5 - √43 )
(student: I don't understand how you got 25?)
25?
This
What's b here?
(student: -10)
-10/2 is?
(same student: 5)
Negative 5
(-5)²? 25
(student: But could you put -10 instead of the b to make it much easier?)
Right, so let's put a -10
(student: Can it be ± √43 + 5) 
Yes, of course.
You can add the 5 at the end as well.
Alright, two more.
We're going to do two more and then we're done.
Aaaand go
So do you like the Captain Kirk thing?
(student: It's very awesome)
(student: Play it in fast motion)
Do you watch more Star Trek
or do you watch more Yay Math?
(students: Yay Math!)
*awesome quick change*
(students: Yay Math!)
Lovely, time to complete the square!
What's that, the next problem?
Oh, sure yeah, say it, say it
x² - 4x (what's that?) - 12
(did she really say that?) = 0
Oh no, aahh muffins, thank you.
I don’t know why they asked me that,
but that’s okay
Time to solve the...
(student: Do you add 12 to both sides?)
Yep, solve by completing the square
add 12 on both sides,
and leave a gap
(student: and so b/4…?)
So you’re getting it, right? You’re getting the number
What do we do to get this number here?
Take our b, not square first,
what do we do first?
(student: divide it by 2 and…)
Divide it by 2 and square it.
So this number, what’s -4/2?
-2, and that squared is?
(student: 4)
So we add 4 to both sides
(*kid sneezes*)
Bless youhuu!
(student: You scared me)
Yay Math
When it's dark and stormy out, Yay Math.
(student: It was a dark and stormy night)
Now this can be factored.
What’s 12 + 4? 16
Here’s x, and remember, 
we said this is, b/2 goes here
so what’s b/2?
(student: is it 2? I mean b?)
what’s b?
(same student: oh, 4)
(another student: -4)
b is -4
(student: so it’s -2 and then square it)
No no no, we don’t do
everything that we did here
this one is just b/2
so what’s b again?
(student: negative 4)
so -4/2 what’s that?
(student: -2)
so here goes -2
(student: that makes sense)
any questions about how we get -2?
-2 here is simply b/2
(student: why don’t you square it then?)
You square it up here
Because, when you foil this out it actually IS squaring the two and that’s what gives us the four
Do you believe that this is the same as this?
(students: yeah)
Are you sure? When you foil this out,
it becomes this, alright
Hand?
(student: do you root both sides?)
Yes, square root both sides.
Now what have you got?
(student: x - 2 = 4)
what else?
(*kids yell different things*)
It’s not just 4
it’s ±4
Real quick explanation:
I know that before you have learned
that √16 is 4. That's true
But √16 means: What two numbers
 multiplied together,
times itself, if you will, 
equals 16?
so 4 and 4 multiply together to make 16
and -4 and -4 also multiply to make 16
So this has two answers: +4 and -4
(student: So technically √16 is -4?)
That's half of the answer
There are two answers to √16,
4 and -4
(student: But you can never have a negative number coming out of a root?)
I know what you're saying, I know what you mean
A square root equation can never
result in a negative number
But the square root of a certain digit,
can result in a negative number.
We're talking about the difference of
x's inside here
and a number like 16.
So what do we do to both sides?
(students: Add 2)
Add 2
x equals, now watch this,
±4 + 2
What this means is this, watch closely
Two answers, 4 + 2
[and] -4 + 2
That's what ± means
It means 4, it also means -4
From this answer we get two paths
What is 4 + 2?
(students: 6)
And what is -4...?
(students: -2)
So these are our two answers
x = 6
x = -2
(student: Do we have to write that?)
Box both, however you want to do it.
(student: Couldn't we just write x = ±4 + 2?)
No, it's not simplified.
Because you can add 2 to 4
Here's the kicker you guys,
look at all this ink
that we spent on completing the square
(student: is there a easier way to do it)
Can this be factored?
(students: yes, oh yeah)
This one can be factored
(student: 6 and -2)
So I heard 6
(another student: +6, -2)
Not really, try again.
(student: -6, +2?)
Why is it -6?
Because this is -4, right?
So this becomes -6, +2
Questions about this?
Foil this quickly in your mind.
x², 2x - 6x, and then -12
x equals what here?
(student: 6 and -2)
x = 6
x = -2
(students: wow, that's so much easier)
There you go! 6 and -2, right here.
So here is the moral of the story before we do our last problem
The moral of the story is: Factoring is the best, quickest, fastest way to solve these types of equations
Now, if you can't factor,
we've learned another method
completing the square
And this last one we're going to do,
see if you can factor it
If you can't factor, then we will complete the square.
(student: Then you do the whole thing?)
Then you do that.
Yes, if you can factor, factor.
For sure.
Look how much time this took.
(student: I will fix your problems)
Me too, in life as well
The actual problems in life
(student: I don't have any problems in life)
(another student: You know 
why I'm not having problems?
Because of Yay Math)
It's all good
I don't have any problems either, well, online
So I don't have any problems, now that I'm a liar
We have established the fact that
life is great!
Can it be factored?
(students: No.)
Ohhh, wait, there's another way to do it!
Yay!
Ready, wait, not yet, now do it.
WAIT, okay go
What are you doing?
(student: plus 7 to both sides)
(student: and leave a space.)
(same student: And then you do the (-2/2)²
What's that number?
(student: 1)
Do we add 1 here too?
Yeah, we do!
(student: why did you put the 7 instead of the 0)
We added 7 to both sides
Because the 7 is not working for us
And we want another number that will
And how did she get the 1?
She divided it by 2
(student: that's -1) and that squared is?
1
-1² is 1
Good, keep going please.
(student: So it's x² -2x+1 = 8)
(same student: So that's (x - 2)²)
Almost, what number goes here?
b/2
So this is b,
so what's -2/2?
(students: -1)
You sure, okay. -1 that's good.
Let's get more people in, thank you.
(student: Root it)
Root it like...
Oh look at the root!
Yay you did it! Boil it!
Stop the jumping jacks, please
You crazy.
It was all a joke, there is no one doing jumping jacks.
What do we do?
x-1 = ±2√2
(student: Do you have to always do that?)
Yes, √8 reduces to 2√2
√4 is?
Plus 1 on both sides.
So it's x = 1 ±2√2
Okay?
(student: 🎶So long, fair well🎶)
Any questions?
Any questions at home?
Do you have questions at home?
Hoooome
Yeah, we're done,
I'm going to cut it now.
Bye.
How dare you?!
