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Math Help - Completing The Square

  1. #1
    Member
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    Completing The Square

    I was wondering if anyone could help? I was looking over some notes about completing the square, and can anyone tell me why this is true?
    x^2+5x+3 =
    (x+5/2)^2-(5/2)^2+3

    I get the first part, (x+5/2)^2 because this makes up a complete square, but why is there a constant that is taken away?
    Thanks alot
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  2. #2
    MHF Contributor
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    (5/2)^2 is taken away because it is added in the (x +5/2)^2

    You see, the incomplete square is (x^2 +5x).
    To make that a perfect square, the square must be completed.
    x^2 +5x +(5/2)^2
    = (x +5/2)^2

    So the (5/2)^2 was added to "complete the square".
    Then,
    (x +5/2)^2 +3
    is not the same anymore as x^2 +5x +3 ----the original expression.
    Because
    (x +5/2)^2 +3
    = x^2 +5x +(5/2)^2 +3.
    There is a (5/2)^2 that was added.

    So to maintain or to make the value of the new expression to equal the value of the original expression, another (5/2)^2 must be taken away from the new expression.
    Hence,
    x^2 +5x +3 = (x +5/2)^2 -(5/2)^2 +3
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  3. #3
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    Sep 2007
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    Good stuff, as iwent through it step by step i understood where i went wrong now..thanks alot
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