What multiplies into -9 and adds up to -8?

Answer 1

-17

Answer 2

(This problem can be done by guess and check. Below is the algebra way.)

Call the two numbers x and y. Then

xy = -9 and x + y = -8

Substituting x = -8 - y into the first equation:

(-8 - y)y = -9

-8y - y^2 = -9

y^2 + 8y - 9 = 0

(y + 9)(y - 1) = 0

Solving this equation gives y = 9 and y = -1, so the two numbers are -9 and 1.