Appendix G - Exercises - Page A12: 21

$x= -1\pm 2i$

Given: $x^{2}+2x+5=0$ Solve using the quadratic formula $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$ Here $a=1, b=2, c=5$ $x=\displaystyle \frac{-2\pm\sqrt{2^{2}-4(1)(5)}}{2(1)}$ $=\frac{-2\pm\sqrt{-16}}{2}$ $=\frac{-2\pm\sqrt{-1\times 16}}{2}$ As we know $\sqrt{-1}=i$, then $=\frac{-2\pm 4i}{2}$ Hence, $x=-1\pm 2i$