Answer
$v = -8, v = -6$
Work Step by Step
Use either the square root method, the quadratic formula or factoring. $$
\begin{aligned}
v^2+14 v & =-48 \\
v^2+14 v+7^2 & =-48+7^2 \\
(v+7)^2 & =1 \\
v+7 & = \pm 1 \\
v & =-7 \pm 1.
\end{aligned}
$$ This gives: $$
\begin{aligned}
&\begin{aligned}
v& =-7-1 \\
& =-8
\end{aligned}\\
&\begin{aligned}
v & =-7+1 \\
& =-6.
\end{aligned}
\end{aligned}
$$ Define the following function and plot it. We see that the zeros are where they should be.
$$
f(v) =v^2+14 v +48.
$$
