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Math Help - completing the square

  1. #1
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    completing the square

    im having trouble working out c in this formula

    The method of completing the square can be used to write the expression:

    5x^2+20x-12 in the form a(x+b)^2+c where a, b and c are constants. What is the value of c?
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  2. #2
    MHF Contributor kalagota's Avatar
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    Quote Originally Posted by offahengaway and chips View Post
    im having trouble working out c in this formula

    The method of completing the square can be used to write the expression:

    5x^2+20x-12 in the form a(x+b)^2+c where a, b and c are constants. What is the value of c?
    5(x^2+4x + r) - 12 -5r

    can you work from here? find that r so that the thing in the parenthesis is a perfect square..
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  3. #3
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    Still a bit confused here, is r=c?
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  4. #4
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    Quote Originally Posted by offahengaway and chips View Post
    Still a bit confused here, is r=c?
    <br />
=5x^2+20x-12

    =5(x^ 2+4x)-12

    =5(x^2 + 4x +4 -4) -12

    =5(x+2)^2-20-12

    Now, finish up.
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  5. #5
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    Just to double check is c= -32?
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  6. #6
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    yes, it is -32.
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  7. #7
    Senior Member bkarpuz's Avatar
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    Exclamation

    In general, for A,B,C\in\mathbb{R} with A\neq0, we have
    Ax^{2}+Bx+C=A\Bigg(x^{2}+\frac{B}{A}x\Bigg)+C
    ...................._ =A\Bigg(x^{2}+\frac{B}{A}x+\bigg(\frac{B}{2A}\bigg  )^{2}-\bigg(\frac{B}{2A}\bigg)^{2}\Bigg)+C
    ...................._ =A\Bigg(x^{2}+\frac{B}{A}x+\bigg(\frac{B}{2A}\bigg  )^{2}\Bigg)+C-\frac{1}{A}\bigg(\frac{B}{2}\bigg)^{2}
    ...................._ =A\Bigg(x+\frac{B}{2A}\Bigg)^{2}+C-\frac{1}{A}\bigg(\frac{B}{2}\bigg)^{2}
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