Answer
The solutions are $10 $ and $-10.$
Work Step by Step
$\displaystyle \frac{x^{2}}{25}-6=-2\qquad$ ...multiply each side with $25$.
$ x^{2}-150=-50\qquad$ ...add $150$ to each side.
$ x^{2}-150+150=-50+150\qquad$ ...simplify
$ x^{2}=100\qquad$ ...take square roots of each side.
$\sqrt{x^{2}}=\sqrt{100}\qquad$ ...simplify.
...When solving an equation of the form $x^{2}=s$ where $s>0$,
we find both the positive and negative solutions.
$x=\pm 10$
