## Elementary Algebra

{$-5-i\sqrt {13},-5+i\sqrt {13}$}
We know that if $x^{2}=a$, then $x=\pm \sqrt{a}$. Thus, we obtain: Step 1: $(x+5)^{2}=-13$ Step 2: $x+5=\pm \sqrt {-13}$ Step 3: $x+5=\pm \sqrt {-1\times13}$ Step 4: $x+5=\pm (\sqrt {-1}\times\sqrt {13})$ Step 5: $x+5=\pm (i\times\sqrt {13})$ [as $i=\sqrt {-1}$] Step 6: $x+5=\pm (i\sqrt {13})$ Step 7: $x=-5\pm (i\sqrt {13})$ Step 8: $x=-5+i\sqrt {13}$ or $x=-5-i\sqrt {13}$ Therefore, the solution set is {$-5-i\sqrt {13},-5+i\sqrt {13}$}.