Answer:
Solutions of x are;
x = -7 + 8i and x = -7 -8i
Step-by-step explanation:
Given the equation: [tex]x^2+14x+17 = -96[/tex]
Add 96 both sides we get;
[tex]x^2+14x+17+96 = 0[/tex]
[tex]x^2+14x+113= 0[/tex]
Using quadratic formula [tex]ax^2+bx+c = 0[/tex] then the solution is given by:
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
On comparing we have;
a= 1, b =14 and c =113
[tex]x = \frac{-14\pm\sqrt{(14)^2-4(1)(113)}}{2(1)}[/tex]
[tex]x = \frac{-14\pm\sqrt{196-452}}{2}[/tex]
or
[tex]x = \frac{-14\pm\sqrt{-256}}{2}[/tex]
Simplify:
[tex]x = \frac{-14\pm 16i}{2}[/tex] ; where i is the imaginary, [tex]i^2= -1[/tex]
or
[tex]x = -7 \pm 8i[/tex]
Therefore, the solution of x are; x = -7 + 8i and x = -7 -8i
