Answer:
x=4+7i and x=4-7i
Step-by-step explanation:
Rewrite the given quadratic equation by completing the square.
x^2-8x=-65
x^2-8x+16=-65+16
x^2-8x+16=-49
(x-4)^2=-49
Now, solve the equation by applying the square root property and isolating x.
(x-4)^2=-49
√(x-4)^2 = √-49
x-4=+7i
x=4+7i
So, the solutions to the given quadratic equation are x+4+7i and x=4-7i.
