For this case what you must do is find the roots of the corresponding polynomial by means of a factorization.
We have then:
x ^ 2-10x + 61
(x- (5 + 6i)) (x- (5-6i))
Checking:
(x- (5 + 6i)) (x- (5-6i))
x ^ 2 - x * (5-6i) - (5 + 6i) x + (5 + 6i) * (5-6i)
x ^ 2 - 5x + 6ix - 5x- 6ix + 25 - 30i + 30i + 36
x ^ 2 -10x + 61
Answer:
(x- (5 + 6i)) (x- (5-6i))
