Question

solve!

x^2 - 12x + 36 = 25

Will give medal!

Answer 1

@wio ? can you help with this one also?

Answer 2

Okay, so... before I said \[
x^2+bx = (x+b/2)^2-(b/2)^2
\]

Answer 3

yeah

Answer 4

For \(x^2-12x\), we have \(b=-12\).

Answer 5

Ok

Answer 6

Can you substitute that value for \(b\) into\[
(x+b/2)^2-(b/2)^2
\]?

Answer 7

yeah
so it would be
x + -12/2)^2 - (12/2)^2

Answer 8

?

Answer 9

Can you simplify it a bit more?

Answer 10

(x -6)^2 - (6)^2

Answer 11

Good, also you can simplify the \(6^2\) as well, we just don't want to foil out \((x-6)^2\).

Answer 12

so (x - 6)(x-6) ?

Answer 13

No, don't foil that part out.

Answer 14

My point is we can simplify it to: \[
(x-6)^2-36
\]

Answer 15

ohh ok

Answer 16

Now, we can say: \[
x^2-12x = (x-6)^2-36
\]

Answer 17

Can you plug that into the red part here?\[
\color{red}{x^2 - 12x} + 36 = 25
\]

Answer 18

I'm kinda confused on what you mean...?

Answer 19

Since we have: \[
x^2-12x = (x-6)^2-36
\]we can swap the two of them whenever we want.
That means we can swap \(x^2-12x\), in the expression \[
\color{red}{x^2-12x}+36=25
\]with \((x-6)^2-36\) to get: \[
[\color{red}{(x-6)^2-36}]+36 = 25
\]

Answer 20

ohh okay

Answer 21

Now, the \(-36+36\) cancel out, and we are left with: \[
(x-6)^2=25
\]

Answer 22

okay,..

Answer 23

When we take the square root of both sides, we end up with: \[
|x-6|=5
\]

Answer 24

Are you familiar with the absolute value bars?

Answer 25

wooaahhh... Is that absolute value? or did you mean parenthesis

Answer 26

Yes, it is the absolute value.

Answer 27

wouldnt you just square root the other side?

Answer 28

I did.

Answer 29

Here is the truth: \[
\sqrt{(\ldots)^2} = |\ldots|
\]

Answer 30

Hmmm. But this is for homework and I dont recall us going over the absolute values... but ok

Answer 31

So \[
\sqrt{25} = |5| = 5
\]

Answer 32

okay

Answer 33

Well, sometimes they forget to mention the absolute value, but it is there.

Answer 34

So do you remember absolute value at all, or do I need to give you a reminder?

Answer 35

no i remember
but now we just add 6?

Answer 36

so x = 11 ?

Answer 37

The absolute value splits it into two equations.

Answer 38

The first equation is the positive one: \[
x-6 = 5
\]The second equation is the negative one: \[
-(x-6)=5
\]

Answer 39

Thank you!

Answer 40

What answers did you get?