Answer
The solutions are $2\sqrt{21}$ and $-2\sqrt{21}$
Work Step by Step
$ x^{2}=84\qquad$ ...take square roots of each side.
$\sqrt{x^{2}}=\sqrt{84}$
...When solving an equation of the form $x^{2}=s$ where $s>0$,
we find both the positive and negative solutions.
$ x=\pm\sqrt{84}\qquad$ ...rewrite $84$ as a product of two factors so that one factor is a perfect square. ($84=4\cdot 21$)
$ x=\pm\sqrt{4\cdot 21}\qquad$ ...use the Product Property $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$
$ x=\pm\sqrt{4}\cdot\sqrt{21}\qquad$ ...evaluate $\sqrt{4} $ ($\sqrt{4}=2$)
$x=\pm 2\sqrt{21}$
