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Math Help - Completing the square

  1. #1
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    Completing the square

    Hi!

    Apparently this is wrong, how do I get the correct form?

    Complete the square for y = -x^2-2x

    \frac{-2}{2(-1)} = 1

    -(x^2-2x) = -(x^2-2x+1)-1

    -(x+1)^2-1
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  2. #2
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    Re: Completing the square

    \displaystyle \begin{align*} y &= -x^2 - 2x \\ &= - \left( x^2 + 2x \right) \\ &= - \left[ x^2 + 2x + 1^2 - 1^2 \right] \\ &= - \left[ \left( x + 1 \right) ^2 - 1 \right] \\ &= - \left( x + 1 \right) ^2 + 1 \end{align*}
    Last edited by Prove It; April 27th 2013 at 10:18 PM.
    Thanks from MarkFL, Unreal and abualabed
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  3. #3
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    Re: Completing the square

    Why is it necessary to factor out the negative 1?

    - \left[ x^2 + 2x + 1^2 - 1^2 \right]
    Could this be written as: - \left[ x^2 + 2x + 1^2\right] - 1^2 OR - \left[ x^2 + 2x + 1^2\right] - 1^2 + 0?
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  4. #4
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    Re: Completing the square

    To complete the square you require that your coefficient of \displaystyle \begin{align*} x^2 \end{align*} is 1, so if your coefficient is something different, you have to take it out as a factor and then complete the square on the leftover stuff.
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