Answer:
(-1-√33)/2, (-1+√33)/2
Explanation:
If one of them is x, then it satisfies ...
x + -8/x = -1
x^2 -8 = -x . . . . . multiply by x
x^2 +x = 8 . . . . . add x+8
x^2 +x + 1/4 = 8+1/4 . . . . complete the square
(x +1/2)^2 = 33/4
x + 1/2 = ±(1/2)√33 . . . . . . take the square root
x = (-1/2)(1 ± √33) . . . . . . . subtract 1/2
The numbers are approximately ...
-3.37228, 2.37228