Answer:
The solutions are x = -7 - 8i and x = -7 + 8i
Step-by-step explanation:
Given equation,
[tex]x^2+14x+17=-96[/tex]
Subtracting 17 on both sides,
[tex]x^2+14x=-113[/tex]
Adding 49 on both sides,
[tex]x^2+14x+49=-64[/tex]
[tex](x+7)^2=-64[/tex]
[tex]x + 7 = \pm\sqrt{-64}[/tex]
[tex]x + 7=\pm 8i[/tex] ( √-1 = i )
[tex]x = -7\pm 8i[/tex]
Thus, the solutions are x = -7 - 8i and x = -7 + 8i
