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Math Help - complete the square

  1. #1
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    complete the square

    Hi everyone,

    I don't remember how to complete the square with a -x^2. Could you please explain to me how to complete the square of 6+4x-4x^2?

    Thank you
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  2. #2
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    Quote Originally Posted by chocolatelover View Post
    explain to me how to complete the square of 6+4x-4x^2?
    6+4x-4x^2=7-(1-4x+4x^2)=7-(1-2x)^2
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  3. #3
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    Quote Originally Posted by chocolatelover View Post
    Hi everyone,

    I don't remember how to complete the square with a -x^2. Could you please explain to me how to complete the square of 6+4x-4x^2?

    Thank you
    Here is one way.

    Remember, you "complete the square" only when the coefficient of the squared variable is 1.

    6 +4x -4x^2
    = -4x^2 +4x +6
    = -4(x^2 -x) +6
    Now, complete the square,
    = -4(x^2 -x +(-1/2)^2 -(-1/2)^2) +6
    = -4[(x -1/2)^2 -1/4] +6
    = -4(x -1/2)^2 +1 +6
    = -4(x -1/2)^2 +7
    = 7 -4(x -1/2)^2 ----------answer.
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