Answer
$x=-\frac{8}{3} \text{ and } x=-\frac{16}{3}$
Work Step by Step
Factor the trinomial:
$$(x+4)(x+4)=\frac{16}{9}\\
(x+4)^2=\frac{16}{9}$$
Take the square root of both sides:
\begin{align*}
\sqrt{(x+4)^2}&=\pm \sqrt{\frac{16}{9}}\\\\
x+4&=\pm \sqrt{\frac{4}{3} \cdot \frac{4}{3}}\\\\
x+4&=\pm \frac{4}{3}
\end{align*}
Subtract $4$ from each side:
\begin{align*}
x&=\pm \frac{4}{3} -4
\end{align*}
Thus, the solutions are:
\begin{align*}
x_1&=\frac{4}{3}-4\\\\
&=\frac{4}{3}-\frac{12}{3}\\\\
&=-\frac{8}{3}
\end{align*}
\begin{align*}
x_2&=-\frac{4}{3}-4\\\\
&=-\frac{4}{3}-\frac{12}{3}\\\\
&=-\frac{16}{3}
\end{align*}
