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Math Help - [SOLVED] Completing the Square

  1. #1
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    [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?
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  2. #2
    Super Member 11rdc11's Avatar
    Joined
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    New Orleans
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    Quote Originally Posted by Zero17 View Post
    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
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  3. #3
    Super Member bigwave's Avatar
    Joined
    Nov 2009
    From
    honolulu
    Posts
    580
    Quote Originally Posted by Zero17 View Post
    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+?
     <br />
x^2+(x+2)^2=10^2<br />

    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 = ()^2so you subtract 1 from both sides.
     x^2 + 2x + 2 -1 = 50 -1

    now you have
      <br />
x^2 + 2x +1 = 49 \rightarrow (x+1)^2 = 49 = 7^2<br />
    Last edited by bigwave; May 28th 2010 at 03:25 PM. Reason: latex
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  4. #4
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    I see, now it makes sense. Thanks guys!
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