x^2 + 14x + 17 = -96
x^2 + 14x + = -113
x^2 + 14x + (14/2)^2 = -133 + (14/2)^2
x^2 + 14x + 49 = -64
(x+7)(x+7) = -64
Find the square root of both sides
(x+7) = √-64
x + 7 = √-64
x = -7 +/- √-64
HOWEVER, the square root of a negative number does not exist among the set of Real Numbers.
The imaginary number "i" replaces the square root of negative 64.
So...
x = -7 +/- 8i
(solution is read as: x equals to negative seven plus or minutes 8i)
