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Math Help - Solve for x

  1. #1
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    Solve for x

    Solve for x.

    (y/x) + p(xy) = (q/s)
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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by magentarita View Post
    Solve for x.

    (y/x) + p(xy) = (q/s)

    Hello again. Another monster, I see.

    \frac{y}{x}+p(xy)=\frac{q}{s}

    First, multiply through by your LCD which is xs.

    sy+psyx^2=qx

    (psy)x^2-qx=-sy

    Now on to completing the square. Divide all terms by (psy)

    x^2-\frac{q}{psy}x=\frac{-sy}{psy}

    x^2-\frac{q}{psy}x+\left(\frac{q}{2psy}\right)^2=-\frac{1}{p}+\left(\frac{q}{2psy}\right)^2

    \left(x-\frac{q}{2psy}\right)^2=\frac{q^2}{4p^2s^2y^2}-\frac{1}{p}

    \left(x-\frac{q}{2psy}\right)^2=\frac{q^2-4ps^2y^2}{4p^2s^2y^2}

    x-\frac{q}{2psy}=\pm\sqrt{\frac{q^2-4ps^2y^2}{4p^2s^2y^2}}

    x=\pm\sqrt{\frac{q^2-4ps^2y^2}{4p^2s^2y^2}}+\frac{q}{2psy}

    x=\frac{\pm\sqrt{q^2-4ps^2y^2}}{2psy}+\frac{q}{2psy}

    x=\frac{\pm\sqrt{q^2-4ps^2y^2}+q}{2psy}

    Well, that's my solution and I'm stickin' with it.
    Last edited by masters; November 22nd 2008 at 03:32 PM.
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  3. #3
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    wow..........

    Quote Originally Posted by masters View Post
    Hello again. Another monster, I see.

    \frac{y}{x}+p(xy)=\frac{q}{s}

    First, multiply through by your LCD which is xs.

    sy+psyx^2=qx

    (psy)x^2-qx=-sy

    Now on to completing the square. Divide all terms by (psy)

    x^2-\frac{q}{psy}x=\frac{-sy}{psy}

    x^2-\frac{q}{psy}x+\left(\frac{q}{2psy}\right)^2=-\frac{1}{p}+\left(\frac{q}{2psy}\right)^2

    \left(x-\frac{q}{2psy}\right)^2=\frac{q^2}{4p^2s^2y^2}-\frac{1}{p}

    \left(x-\frac{q}{2psy}\right)^2=\frac{q^2-4ps^2y^2}{4p^2s^2y^2}

    x-\frac{q}{2psy}=\pm\sqrt{\frac{q^2-4ps^2y^2}{4p^2s^2y^2}}

    x=\pm\sqrt{\frac{q^2-4ps^2y^2}{4p^2s^2y^2}}+\frac{q}{2psy}

    x=\frac{\pm\sqrt{q^2-4ps^2y^2}}{2psy}+\frac{q}{2psy}

    x=\frac{\pm\sqrt{q^2-4ps^2y^2}+q}{2psy}

    Well, that's my solution and I'm stickin' with it.
    You really went all the way this tme around.
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