Answer
$g=9,-16$
Work Step by Step
$g^2+7g=144$
Compare it with the standard form of quadratic equation $ax^2+bx+c$, we have $a=1, b=7$
Therefore, $b^2=4ac$ $\implies$ $c=\dfrac{b^2}{4a}$
Thus, $c=\dfrac{b^2}{4a}=\dfrac{(7)^2}{4}=\frac{49}{4}$
To complete the square, add $\frac{49}{4}$ on both sides.
$g^2+7g+\frac{49}{4}=144+\frac{49}{4}$
$\implies (g+\frac{7}{2})^2=\frac{625}{4}$
$\implies (g+\frac{7}{2})=\frac{625}{4}$
and
$\implies (g+\frac{7}{2})=-\frac{625}{4}$
or, $g=9,-16$
