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Math Help - Completing the Square help

  1. #1
    Newbie
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    Mar 2010
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    Completing the Square help

    Hey guys,

    I need help completing this square:

    x^2 + 3x + 2

    Ive been following tips online, and ive gotten as far as:

    x^2 + 3x + 9/4 = 1/4

    but i cant get any further because no matter where i go to i dont understand the next step.

    can anybody help?

    thanks in advance
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  2. #2
    Senior Member
    Joined
    Nov 2008
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    Hi.

    Quote Originally Posted by Mitch281008 View Post
    Hey guys,

    I need help completing this square:

    x^2 + 3x + 2

    Ive been following tips online, and ive gotten as far as:

    x^2 + 3x + 9/4 = 1/4

    but i cant get any further because no matter where i go to i dont understand the next step.

    can anybody help?

    thanks in advance
    WEll, there only is one step missing.

    Do you know that

    (a+b)^2 = a^2+2ab+b^2 ?

    Now consider x^2 + 3x + 9/4

    What we know is a^2=x^2, 2ab = 3x and b^2 = 9/4

    We know that a = x and b^2 = 9/4. What is b? b is equal to \sqrt{ 9/4 } = 3/2

    So we have

    [ (a+b)^2 = ] (x+3/2)^2

    Solving (x+3/2)^2 leads to x^2+2*\frac{3}{2}x + (\frac{3}{2})^2 = x^2+3x+9/4

    Thus our calculation is correct.
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  3. #3
    Like a stone-audioslave ADARSH's Avatar
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    Simple steps are

    x^2 + 3x + 2


    x^2 + \frac{2*3x}{2} + \frac{9}{4} - \frac{1}{4}

    x^2 + \frac{2*3x}{2} + (\frac{3}{2})^2 - \frac{1}{4}

    This is of the form

    a^2 + 2ab + b^2 -c

    it can be written as

    (a+b)^2 -c

    (x+\frac{3}{2})^2 - \frac{1}{4}

    Game Over XX

    EDIT: Rapha was quicker ..... and correct ofcourse
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  4. #4
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    ok thanks alot for that. im still not really confident with them, but that does help explain.

    cheers
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