Answer
$q=-0.38,-2.62$
Work Step by Step
$q^2+3q+1=0$
or, $q^2+3q=-1$
Compare it with the standard form of quadratic equation $ax^2+bx+c$, we have $a=1, b=3$
To complete the square, add $\frac{9}{4}$ on both sides.
$q^2+3q+\frac{9}{4}=-1+\frac{9}{4}$
$\implies (q+\frac{3}{2})^2=\frac{5}{4}$
$\implies (q+1.5)^2=\frac{5}{4}$
$\implies (q+1.5)=1.12$
and
$\implies (q+1.5)=-1.12$
or, $q=-0.38,-2.62$
