What multiplies to -10 but adds up to -56?

Answer 1

-66

Answer 2

a*b=-10

a+b=-56, or a=-b-56

Substitute for a in the first equation with the second equation:

(-b-56)*b=-10

-b2-56b+10=0

b2+56b-10=0

Solve for b (quadratic equation):

b = (56 +- (562 + 40).5)/2 = .178, 56.178

Now solve for a=-b-56

(a,b) = (-56.178,.178),(-112.178,56.178)

The second (a,b) pair doesn't work when substituted into a*b=-10, so the only answer is (a,b) = (-56.178,.178).