Answer
$\left\{-\dfrac{5}{2} - \dfrac{\sqrt{37}}{2}, -\dfrac{5}{2}+\dfrac{\sqrt{37}}{2}\right\}$
Work Step by Step
Add $3$ to both sides:
$$x^2+5x=3$$
Recall:
To complete the square of $x^2+bx$, add $\left(\dfrac{b}{2}\right)^2$.
Complete the square by adding $\left(\dfrac{5}{2}\right)^2$ to both sides of the equation to obtain:
\begin{align*}
x^2+5x+\left(\frac{5}{2}\right)^2&=3+\left(\frac{5}{2}\right)^2\\\\
x^2+5x+\frac{25}{4}&=3+\frac{25}{4}\\\\
\left(x+\frac{5}{2}\right)^2&=\frac{12}{4}+\frac{25}{4}\\\\
\left(x+\frac{5}{2}\right)^2&=\frac{37}{4}\\\\
\end{align*}
Take the square root of both sides:
\begin{align*}
\sqrt{\left(x+\frac{5}{2}\right)^2}&=\pm\sqrt{\frac{37}{4}}\\\\
x+\frac{5}{2}&=\pm\frac{\sqrt{37}}{2}\\\\
x&=-\frac{5}{2}\pm\frac{\sqrt{37}}{2}\\\\
\end{align*}
Thus, the solution set is:
$$\left\{-\dfrac{5}{2} - \dfrac{\sqrt{37}}{2}, -\dfrac{5}{2}+\dfrac{\sqrt{37}}{2}\right\}$$
