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: [ \begin{align*} 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} \end{align*} ]

Step3: Simplify square - root of negative number

Since $\sqrt{-64}=\sqrt{64}\times\sqrt{-1}=8i$, then [ \begin{align*} x&=\frac{-2\pm8i}{2}\ &=-1\pm4i \end{align*} ]

Answer:

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