Answer
$v=7,-2$
Work Step by Step
$2v^2-10v-20=8$
Re-write the equations as: $v^2-5v-10=4$
Compare it with the standard form of quadratic equation $ax^2+bx+c$, we have $a=1, b=-5$
Therefore, $b^2=4ac$ $\implies$ $c=\dfrac{b^2}{4a}$
Thus, $c=\dfrac{b^2}{4a}=\dfrac{(-5)^2}{4}=\dfrac{25}{4}$
To complete the square, add $\dfrac{25}{4}$ on both sides.
$v^2-5v-10+\dfrac{25}{4}=4+\dfrac{25}{4}$
$\implies (v-\dfrac{5}{2})^2=\dfrac{81}{4}$
$\implies (v-\dfrac{5}{2})= \dfrac{9}{2}$
and
$\implies (v-\dfrac{5}{2})= -\dfrac{9}{2}$
or, $v=7,-2$
