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Math Help - Completing the square with fraction as coefficient of x^2

  1. #1
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    Completing the square with fraction as coefficient of x^2

    Hi!

    Complete the square for \frac12x^2-x+3

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

    \frac12(x^2 - 2x + 1 - 1) + 3

    \frac12(x-1)^2 - 2
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  2. #2
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    Re: Completing the square with fraction as coefficient of x^2

    You make life difficult on yourself if you skip steps. The first thing to do is to take out \displaystyle \begin{align*} \frac{1}{2} \end{align*} as a factor, then complete the square on everything left over, then multiply that factor back through.
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    Re: Completing the square with fraction as coefficient of x^2

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

    \frac12(x^2 - 2x) + 3

    \frac12\left[(x^2 - 2x + 1 - 1) + 3\right]

    \frac12(x-1)^2 - 1 + 3

    \frac12(x-1)^2 + 2
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    Re: Completing the square with fraction as coefficient of x^2

    I'm not giving any more help until you learn to follow the instructions you've been given.
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  5. #5
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    Re: Completing the square with fraction as coefficient of x^2

    My solution is what I understand from the instructions given.

    Quote Originally Posted by Prove It
    The first thing to do is to take out \frac12 as a factor
    Factoring \frac12 from the x^2 and x terms: \frac12\left[(x^2 - 2x + 6)\right]

    Quote Originally Posted by Prove It
    then complete the square on everything left over
    \frac12(x^2 - 2x + 1 - 1 + 6)

    \frac12\left[(x-1)^2 + 5\right]

    Quote Originally Posted by Prove It
    then multiply that factor back through.
    \frac12(x-1)^2 + \frac52
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  6. #6
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    Re: Completing the square with fraction as coefficient of x^2

    And this is correct. Well done.
    Thanks from Unreal
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