What times what is 18 and added is -11?

Answer 1

Let a and b be the two numbers such that

ab = 18 and a+b = -11

Rearrange terms of a+b = -11 so that a = -11 - b. (1)

Use this in ab=18 to get (-11 - b) *b = 18

Simplify to get -11b -b² = 18

Multiply both sides by -1 to get b² + 11b = -18

Add 18 to both sides to get b² + 11b +18 = 0

You can use the quadratic formula to see that the only reasonable solution for b is -9, because

-9² + (-9)*11 + 18 = 81 -99 +18 = -18 + 18 = 0.

We know that a+b = -11, so since b = -9, a = -11 - (-9) = -11+9 = -2.

The solution following this thread is a=-2 and b=-9.

NOTE: Suppose in (1) you solved for b instead of a and then followed the next steps. You'd find that

a = -9 and b = -2.

Thus there are 2 possible solutions, (a=-2, b=-9) and (a=-9, b=-2) satisfying both equations.