Answer
$x=100$ and $x=-50$
Work Step by Step
$\dfrac{x^{2}}{x+100}=50$
Take $x+100$ to multiply the right side of the equation:
$x^{2}=50(x+100)$
Evaluate the product on the right:
$x^{2}=50x+5000$
Rewrite the equation by taking all terms to the left side:
$x^{2}-50x-5000=0$
Solve using the quadratic formula, knowing that $a=1$, $b=-50$ and $c=-5000$:
$x=\dfrac{-(-50)\pm\sqrt{(-50)^{2}-4(1)(-5000)}}{2(1)}=...$
$...=\dfrac{50\pm\sqrt{2500+20000}}{2}=\dfrac{50\pm\sqrt{22500}}{2}=\dfrac{50\pm150}{2}$
So, our two solutions are:
$x=\dfrac{50+150}{2}=100$ and $x=\dfrac{50-150}{2}=-50$
