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Math Help - Completing the square.

  1. #1
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    Completing the square.

    Original problem: x/12=5/2x+7 (in proportion view) and i got it to: x^2 + 7x=60 and then x^2 + 7/2x = 30 Need help wit the rest please.
    Last edited by mr fantastic; November 21st 2011 at 04:12 PM. Reason: Title etc.
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  2. #2
    MHF Contributor Siron's Avatar
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    Re: Completing the square!?!?

    Quote Originally Posted by livfaure View Post
    Original problem: x/12=5/2x+7 (in proportion view) and i got it to: x^2 + 7x=60 and then x^2 + 7/2x = 30 NEED HELP WITH THE REST PLEASE!!
    It's not correct! It has to be:
    \frac{x}{12}=\frac{5}{2x}+7 \Leftrightarrow \frac{x^2}{6}=5+14x \Leftrightarrow x^2=30+84x \Leftrightarrow x^2-84x-30=0

    Now you have to reform it to (=completing the square):
    (x-a)^2+b
    where you have to determine a and b.

    Can you proceed?
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  3. #3
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    Re: Completing the square!?!?

    No, im sory i guess i wasnt clear enough its like this (see picture) its number 34
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    Re: Completing the square!?!?

    link to pic is a no show.



    is this your equation ...

    x/12 = 5/(2x+7) my parentheses added

    \frac{x}{12} = \frac{5}{2x+7}

    ???
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  5. #5
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    Re: Completing the square!?!?

    yes, that it is!
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  6. #6
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    Re: Completing the square!?!?

    Quote Originally Posted by livfaure View Post
    yes, that it is!
    In that case cross multiply: x(2x+7) = 60 \Leftrightarrow 2x^2+7x = 60 \Leftrightarrow x^2 + \dfrac{7}{2}x = 30

    The last form is easiest for completing the square. When I complete the square I divide the middle term by 2 (since when we FOIL we get 2ab as the middle term) and add \frac{b^2}{4} (before dividing by 2) to both sides to get the constant term

    x^2 + \dfrac{7}{2}x + \dfrac{49}{16} = 30 + \dfrac{49}{16}


    In terms of the quadratic formula: x^2 + \dfrac{b}{a} + \dfrac{b^2}{4a^2} = -c + \dfrac{b^2}{4a^2} = \left(x+ \dfrac{b}{2a}\right)^2 = \dfrac{b^2}{4a^2} - c
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