Answer
The solutions are $4\sqrt{7} $ and $-4\sqrt{7}$
Work Step by Step
$ 4p^{2}=448\qquad$ ...divide each side with $4$
$ p^{2}=112\qquad$ ...take square roots of each side.
$\sqrt{p^{2}}=\sqrt{112}\qquad$ ...simplify
...When solving an equation of the form $x^{2}=s$ where $s>0$,
we find both the positive and negative solutions.
$ p=\pm\sqrt{112}\qquad$ ...rewrite $112$ as a product of two factors so that one factor is a perfect square. ($112=16\cdot 7$)
$ p=\pm\sqrt{16\cdot 7}\qquad$ ...use the Product Property $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$
$ p=\pm\sqrt{16}\cdot\sqrt{7}\qquad$ ...evaluate $\sqrt{16} $ ($\sqrt{16}=4$)
$p=\pm 4\sqrt{7}$
