Answer
The solutions are $5\sqrt{2}$ and $-5\sqrt{2}$.
Work Step by Step
$ a^{2}=50\qquad$ ...take square roots of each side.
$\sqrt{a^{2}}=\sqrt{50}$
...When solving an equation of the form $x^{2}=s$ where $s>0$,
we find both the positive and negative solutions.
$ a=\pm\sqrt{50}\qquad$ ...rewrite $50$ as a product of two factors so that one factor is a perfect square. ($50=25\cdot 2$)
$ a=\pm\sqrt{25\cdot 2}\qquad$ ...use the Product Property $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$
$ a=\pm\sqrt{25}\cdot\sqrt{2}\qquad$ ...evaluate $\sqrt{25} $ ($\sqrt{25}=5$)
$a=\pm 5\sqrt{2}$
