solve: $x^{2}+2x + 17=0$\na $x=-1 + 4i$ or $x=-1-4i$\nb $x=-1 + 8i$ or $x=-1-8i$\nc $x=1 + 8i$ or…

Explanation:

Step1: Identify coefficients

For the quadratic equation $x^{2}+2x + 17=0$, we have $a = 1$, $b = 2$, $c = 17$.

Step2: Use quadratic formula

The quadratic formula is $x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. Substitute the values: $x=\frac{-2\pm\sqrt{2^{2}-4\times1\times17}}{2\times1}=\frac{-2\pm\sqrt{4 - 68}}{2}=\frac{-2\pm\sqrt{- 64}}{2}$.

Step3: Simplify the square - root

Since $\sqrt{-64}=\sqrt{64\times(-1)} = 8i$, then $x=\frac{-2\pm8i}{2}$.

Step4: Simplify the expression

$x=\frac{-2}{2}\pm\frac{8i}{2}=-1\pm4i$.

Answer:

A. $x=-1 + 4i$ or $x=-1-4i$