How do I solve this equation How do I solve this equation, I keep getting the wrong answer.
$$ \frac{-2x^2+50}{\sqrt{50-x^2}} = 1 $$
Thank you

We have:
$$\sqrt{50 - x^2} = 50 - 2x^2$$
Eliminating the square root and opening the brackets:
$$50 - x^2 = 4x^4 - 200x^2 + 2500$$
Make it more simple:
$$-4x^4 + 199x^2 - 2450 = 0$$
Substitute $y = x^2$, simplifying and find full square:
$$\left(y - \dfrac{199}{8}\right)^2 = \dfrac{401}{64}$$
So, there is two solutions:
$$y = \dfrac{199}{8} \pm \dfrac{\sqrt{401}}{8}$$
So, there is 4 solutions for $x$:
$$x = \pm\sqrt{\dfrac{199}{8} - \dfrac{\sqrt{401}}{8}}\tag{1}$$
$$x = \pm\sqrt{\dfrac{199}{8} + \dfrac{\sqrt{401}}{8}}\tag{2}$$
Substitution the solution for $x$ into original equations shows the correcteness of $(1)$ solutions and incorrectness of solutions $(2)$.
Finally:
$$x_1 = \sqrt{\dfrac{199}{8} - \dfrac{\sqrt{401}}{8}}\approx 4.7299\qquad x_2 = -\sqrt{\dfrac{199}{8} - \dfrac{\sqrt{401}}{8}}\approx -4.7299$$
