Chapter 9 - Quadratic Functions and Equations - 9-5 Completing the Square - Practice and Problem-Solving Exercises - Page 564: 15

$m=-5.76,-10.24$

$m^2+16m=-59$ Compare 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, $m=-5.76,-10.24$