Answer
$m=-5.76,-10.24$
Work Step by Step
$m^2+16m=-59$
Comparing it with the standard form of quadratic equation $ax^2+bx+c$, we have $a=1, b=16$
Therefore, $b^2=4ac$ $\implies$ $c=\dfrac{b^2}{4a}$
Thus, $c=\dfrac{b^2}{4a}=\dfrac{(16)^2}{4}=64$
To complete the square, add $4$ on both sides.
$m^2+16m+64=-59+64$
$\implies (m+8)^2=5$
$\implies m+8=2.24$
and
$\implies m+8=-2.24$
or, $m=-5.76,-10.24$
