Answer
$m=-5\displaystyle \pm\frac{\sqrt{2}}{2}$
Work Step by Step
$ 16(m+5)^{2}=8\qquad$ ...divide the entire expression with $16$.
$(m+5)^{2}=\displaystyle \frac{1}{2}\qquad$ ...take square roots of each side.
$ m+5=\pm\sqrt{\frac{1}{2}}\qquad$ ...add $-5$ to each side.
$ m=-5\displaystyle \pm\frac{1}{\sqrt{2}}\qquad$ ...rationalize the radical by multiplying both the numerator and denominator with $\sqrt{2}$.
$\displaystyle \frac{1}{\sqrt{2}}=\frac{1\cdot\sqrt{2}}{\sqrt{2}\cdot\sqrt{2}}=\frac{\sqrt{2}}{2}$
$m=-5\displaystyle \pm\frac{\sqrt{2}}{2}$
