# Thread: [SOLVED] Completing the Square

1. ## [SOLVED] Completing the Square

Hi all, this is my first post here.

Ok, I'm using a math program in college (I forgot everything I learned in highschool math and am retaking courses to get up tp speed) for some algebra level math. I'm currently working on a section called "completing the square". Everything was going fine until this problem:

http://img294.imageshack.us/img294/2425/whatm.png

I wasn't sure how to go about doing the problem, and this is how the program responded. Normally I will pick up on how to do something after it shows me, but I'm not sure how it went about doing this one. First off, the problem started as:

X^2+(x+2)^2=10^2. Where did the 4X come from? The other part I'm a bit confused about is, a few lines down, the program goes from:

x^2+2x+2=50
to:
X^2+2x+?=48+?

It then changes it to a 1. What's up with that? I don't recall ever doing that in highschool. The program isn't explaining how it did any of this either, other than what you see here. Can someone enlighten me?

2. Originally Posted by Zero17
Hi all, this is my first post here.

Ok, I'm using a math program in college (I forgot everything I learned in highschool math and am retaking courses to get up tp speed) for some algebra level math. I'm currently working on a section called "completing the square". Everything was going fine until this problem:

http://img294.imageshack.us/img294/2425/whatm.png

I wasn't sure how to go about doing the problem, and this is how the program responded. Normally I will pick up on how to do something after it shows me, but I'm not sure how it went about doing this one. First off, the problem started as:

X^2+(x+2)^2=10^2. Where did the 4X come from? The other part I'm a bit confused about is, a few lines down, the program goes from:

x^2+2x+2=50
to:
X^2+2x+?=48+?

It then changes it to a 1. What's up with that? I don't recall ever doing that in highschool. The program isn't explaining how it did any of this either, other than what you see here. Can someone enlighten me?
$(x+2)^2 = (x+2)(x+2)$

Now just use foil and you get

$x^2 +4x +4$

3. Originally Posted by Zero17
x^2+(x+2)^2=10^2. Where did the 4X come from? The other part I'm a bit confused about is, a few lines down, the program goes from:

x^2+2x+2=50
to:
X^2+2x+?=48+?
$
x^2+(x+2)^2=10^2
$

the $4x$ comes from expanding $(x+2)^2$
which become $x^2 + 4x + 4$

after simplifing you get $x^2 + 2x + 2 = 50$
however this is not in the format of $( )^2 = ()^2$so you subtract 1 from both sides.
$x^2 + 2x + 2 -1 = 50 -1$

now you have
$
x^2 + 2x +1 = 49 \rightarrow (x+1)^2 = 49 = 7^2
$

4. I see, now it makes sense. Thanks guys!