Answer
$\left\{-\dfrac{4}{5}, \dfrac{2}{5}\right\}$
Work Step by Step
Factor the trinomial to obtain:
\begin{align*}
(5x+1)(5x+1)&=9\\
(5x+1)^2&=3^2
\end{align*}
Take the square root of both sides:
\begin{align*}
\sqrt{(5x+1)^2}&=\pm\sqrt{3^2}\\\\
5x+1&=\pm3\\\\
5x&=-1\pm 3\\\\
\frac{5x}{5}&=\frac{-1\pm3}{5}\\\\
x&=-\frac{1}{5} \pm \frac{3}{5}
\end{align*}
Split the solutions to obtain:
\begin{align*}
x_1&=-\frac{1}{5}-\frac{3}{5}\\
&=-\frac{4}{5}
\end{align*}
\begin{align*}
x_2&=-\frac{1}{5}+\frac{3}{5}\\
&=\frac{2}{5}
\end{align*}
