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Math Help - Solving a quadratic equation by completing the square

  1. #1
    tac
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    Solving a quadratic equation by completing the square

    Once the middle term is not an even number I get very confused.

    This is what I have so far:

    x^2 + 5x + 5 = 0

    x^2 + 5x + (5/2)^2 = -5 = (5/2)^2

    (x + 5/2)^2 = -5 + 25/4

    (x + 5/2) = -20/4 + 25/4 = 5/4

    I don't know if I am on the right track or doing completely wrong.
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  2. #2
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    Re: Solving a quadratic equation by completing the square

    You are completely on the right track except the last line
    x+5/2 = sqrt(5)/2 or x+5/2 = -sqrt(5)/2
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  3. #3
    Member Furyan's Avatar
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    Re: Solving a quadratic equation by completing the square

    Hello,

    You might find it less confusing if you complete the square first and then solve for  x.

    x^2 +5x+5 = 0

    (x + \dfrac{5}{2})^2 -  (\dfrac{5}{2})^2 +5 = 0

    (x + \dfrac{5}{2})^2 -  \dfrac{25}{4} +\dfrac {20}{4} = 0

    (x + \dfrac{5}{2})^2 -  \dfrac{5}{4} = 0

    Now solve for  x.
    Last edited by Furyan; December 1st 2012 at 03:59 PM.
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