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Math Help - Solving a 6-Variable Equation with Square Roots for X

  1. #1
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    Solving a 6-Variable Equation with Square Roots for X

    I hope I'm in the right forum, since I'm trying to solve for x.

    I have an equation with 6 variables (a through e and x):
    \frac{-d+\sqrt{d^2+2xa}}{x}=\frac{-e+\sqrt{e^2+2b\sqrt{c^2-x^2}}}{\sqrt{c^2-x^2}}
    and I need to know what x is in terms of the other 5 variables.

    When d=0 and e=0 (which is sometimes but not always true):
    \frac{\sqrt{2xa}}{x}=\frac{\sqrt{2b\sqrt{c^2-x^2}}}{\sqrt{c^2-x^2}}
    I was able to solve for x:
    x=\frac{ac}{\sqrt{b^2+a^2}}

    However, when it's not true that d=0 and e=0, those addends throw me off (they make it harder to just square the sqrt's away). I find myself bumbling around back and forth, and I feel like there's some rule or simplification that I'm not applying.

    Can anyone lend some advice?

    I got this far and realized I don't know what to do:
    (-d+\sqrt{d&2+2xa})(\sqrt{c^2-x^2})+2xe=\frac{2x^2b}{-d+\sqrt{d^2+2xa}}
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  2. #2
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    That's a nasty eqn to solve.

    Do you have to solve it by hand? I would use a computer software package like maple to solve this. It will solve it, if it can be solved!
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  3. #3
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    Quote Originally Posted by pickslides View Post
    That's a nasty eqn to solve.

    Do you have to solve it by hand? I would use a computer software package like maple to solve this. It will solve it, if it can be solved!
    Actually, I don't have to solve it by hand. I tried WolframAlpha, but it spat out some really long solutions for x, and I don't think they are the ones I'm looking for. See, I had tried it before, typing in the simplified equation where e=d=0:
    sqrt(2xa)/x=sqrt(2*sqrt(c^2-x^2)*b)/sqrt(c^2-x^2)
    and I'm pretty sure it gave me really long solutions too, but now it seems to be giving the correct answer... I wonder if it was just running out of time before.
    In any case, when I punch in the more complex one:
    (-d+sqrt(d^2+2xa))/x=(-e+sqrt(e^2+2b*sqrt(c^2-x^2)))/sqrt(c^2-x^2)
    it gives me really long solutions for x and says "Computation timed out. No more results available."
    Last edited by BlueTheCow; February 2nd 2011 at 09:22 PM.
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