solve for x in the equation $x^{2}+14x + 17=-96$.\n$x=-7pm4sqrt{6}i$\n$x=-7pm8i$\n$x=7pm4sqrt{6}i$\n$x=7pm8i$

Explanation:

Step1: Rewrite in standard form

First, rewrite the equation $x^{2}+14x + 17=-96$ as $x^{2}+14x+113 = 0$. The general - form of a quadratic equation is $ax^{2}+bx + c = 0$, where $a = 1$, $b = 14$, and $c = 113$.

Step2: Apply the quadratic formula

The quadratic formula is $x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. Substitute $a = 1$, $b = 14$, and $c = 113$ into the formula: [ \begin{align*} x&=\frac{-14\pm\sqrt{14^{2}-4\times1\times113}}{2\times1}\ &=\frac{-14\pm\sqrt{196 - 452}}{2}\ &=\frac{-14\pm\sqrt{-256}}{2} \end{align*} ] Since $\sqrt{-256}=\sqrt{256}\times\sqrt{-1}=16i$, then $x=\frac{-14\pm16i}{2}$.

Step3: Simplify the expression

[ \begin{align*} x&=\frac{-14\pm16i}{2}\ &=-7\pm8i \end{align*} ]

Answer:

B. $x=-7\pm8i$