Answer
$-10$; $-4$
Work Step by Step
Given\begin{equation}
4(x+7)^2-36 =0.
\end{equation} Apply the square root property to solve:
\begin{equation}
\begin{aligned}
4(x+7)^2-36 & =0 \\
4(x+7)^2 & =36 \\
(x+7)^2 & =\frac{36}{4} \\
(x+7)^2 & =9 \\
(x+7) & = \pm \sqrt{9} \\
x+7 & = \pm 3 \\
x & =-7 \pm 3.
\end{aligned}
\end{equation} This gives: \begin{equation}
\begin{aligned}
x & =-7-3 \\
& =-10 \\
x & =-7+3 \\
& =-4.
\end{aligned}
\end{equation} Check:
\begin{equation}
\begin{array}{r}
4(-4+7)^2-36\stackrel{?}{=}0 \\
4(9)-36\stackrel{?}{=}0 \\
0=0\checkmark\\\\
4(-10+7)^2-36\stackrel{?}{=}0 \\
4(9)-36\stackrel{?}{=}0 \\
0=0\checkmark.
\end{array}
\end{equation} The solution is:$$x=-10,\quad x=-4.$$
