Answer
$\left\{ -3-2i,-3+2i \right\}$
Work Step by Step
Using $\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$ (or the Quadratic Formula), the solutions of the given quadratic equation, $
x^2+6x+13
,$ are
\begin{array}{l}\require{cancel}
\dfrac{-(6)\pm\sqrt{(6)^2-4(1)(13)}}{2(1)}
\\\\=
\dfrac{-6\pm\sqrt{36-52}}{2}
\\\\=
\dfrac{-6\pm\sqrt{-16}}{2}
\\\\=
\dfrac{-6\pm\sqrt{-1}\cdot\sqrt{(4)^2}}{2}
\\\\=
\dfrac{-6\pm i\cdot4}{2}
\\\\=
\dfrac{-6\pm 4i}{2}
\\\\=
\dfrac{2(-3\pm 2i)}{2}
\\\\=
\dfrac{\cancel{2}(-3\pm 2i)}{\cancel{2}}
\\\\=
-3\pm 2i
.\end{array}
Hence, the solutions are $
\left\{ -3-2i,-3+2i \right\}
.$