# [SOLVED] Completing the Square

• May 28th 2010, 02:54 PM
Zero17
[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?
• May 28th 2010, 03:21 PM
11rdc11
Quote:

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?

$\displaystyle (x+2)^2 = (x+2)(x+2)$

Now just use foil and you get

$\displaystyle x^2 +4x +4$
• May 28th 2010, 03:21 PM
bigwave
Quote:

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+?

$\displaystyle x^2+(x+2)^2=10^2$

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

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

now you have
$\displaystyle x^2 + 2x +1 = 49 \rightarrow (x+1)^2 = 49 = 7^2$
• May 28th 2010, 03:49 PM
Zero17
I see, now it makes sense. Thanks guys!