Question

solve for x in the equation $x^{2}+14x + 17=-96$.\
\\(\bigcirc\\) $x = -7\pm4\sqrt{6}i$\
\\(\bigcirc\\) $x = -7\pm8i$\
\\(\bigcirc\\) $x = 7\pm4\sqrt{6}i$\
\\(\bigcirc\\) $x = 7\pm8i$

Explanation:

Step1: Rearrange equation to standard form

$x^2 + 14x + 17 + 96 = 0$
$x^2 + 14x + 113 = 0$

Step2: Complete the square

$(x^2 + 14x + 49) + 113 - 49 = 0$
$(x + 7)^2 + 64 = 0$

Step3: Isolate squared term

$(x + 7)^2 = -64$

Step4: Solve for x

$x + 7 = \pm\sqrt{-64} = \pm8i$
$x = -7 \pm8i$

Answer:

$x = -7 \pm 8i$