# Thread: Solving a 6-Variable Equation with Square Roots for X

1. ## 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.

I got this far and realized I don't know what to do:
$(-d+\sqrt{d&2+2xa})(\sqrt{c^2-x^2})+2xe=\frac{2x^2b}{-d+\sqrt{d^2+2xa}}$

2. 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!

3. Originally Posted by pickslides
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."