Let the two numbers be x and y, then
xy = 99 . . . (1)
x + y = -34 . . . (2)
From (2), x = -34 - y . . . (3)
Putting (3) into (1), gives
(-34 - y)y = 99
-34y - y^2 = 99
y^2 + 34y + 99 = 0
\(y= \frac{-34\pm \sqrt{34^2-(4\times99)} }{2} = \frac{-34\pm \sqrt{760} }{2} = \frac{-34\pm 2\sqrt{190} }{2} = -17\pm\sqrt{190}\)
Therefore, the two numbers are \(-17+\sqrt{190}\) and \(-17-\sqrt{190}\)
