# [SOLVED] Completing the Square

#### 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?

#### 11rdc11

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

$$\displaystyle x^2 +4x +4$$

• Zero17

#### bigwave

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
$$\displaystyle x^2 + 2x +1 = 49 \rightarrow (x+1)^2 = 49 = 7^2$$

Last edited:
• Zero17

#### Zero17

I see, now it makes sense. Thanks guys!