Question

Solve for x in the equation x² + 14x + 17 = - 96

Answer 1

Answer:

Solutions of x are;

x = -7 + 8i and x = -7 -8i

Step-by-step explanation:

Given the equation: $x^2+14x+17 = -96$

Add 96 both sides we get;

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

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

Using quadratic formula $ax^2+bx+c = 0$ then the solution is given by:

$x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}$

On comparing we have;

a= 1,  b =14 and c =113

$x = \frac{-14\pm\sqrt{(14)^2-4(1)(113)}}{2(1)}$

$x = \frac{-14\pm\sqrt{196-452}}{2}$

or

$x = \frac{-14\pm\sqrt{-256}}{2}$

Simplify:

$x = \frac{-14\pm 16i}{2}$ ;  where i is the imaginary, $i^2= -1$

or

$x = -7 \pm 8i$

Therefore,  the solution of x are;  x = -7 + 8i and x = -7 -8i