Chapter 9 - Quadratic Functions and Equations - 9-5 Completing the Square - Practice and Problem-Solving Exercises - Page 564: 16

$q=2,5,-6.5$

$q^2+4q=16$ Compare it with the standard form of quadratic equation $ax^2+bx+c$, we have $a=1, b=4$ Therefore, $b^2=4ac$ $\implies$ $c=\dfrac{b^2}{4a}$ Thus, $c=\dfrac{b^2}{4a}=\dfrac{(4)^2}{4}=4$ To complete the square, add $4$ on both sides. $q^2+4q+4=16+4$ $\implies (q+2)^2=20$ $\implies q+2=4.5$ and $\implies q+2=-4.5$ or, $q=2,5,-6.5$