Answer
$\left\{ \dfrac{-5-\sqrt{17}}{2},\dfrac{-5+\sqrt{17}}{2} \right\}$
Work Step by Step
The standard form of the given equation, $
x^2+5x=-2
,$ is
\begin{array}{l}\require{cancel}
x^2+5x+2=0
.\end{array}
Using $\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$ (or the Quadratic Formula), the solutions of the quadratic equation, $
x^2+5x+2=0
,$ are
\begin{array}{l}\require{cancel}
\dfrac{-(5)\pm\sqrt{(5)^2-4(1)(2)}}{2(1)}
\\\\=
\dfrac{-5\pm\sqrt{25-8}}{2}
\\\\=
\dfrac{-5\pm\sqrt{17}}{2}
.\end{array}
Hence, the solutions are $
\left\{ \dfrac{-5-\sqrt{17}}{2},\dfrac{-5+\sqrt{17}}{2} \right\}
.$
