Question

What multiplies to be -18 and adds to be -9?

Answer 1

IMPORTANT:
If you're trying to factor a quadratic in Algebra I:
There are no two integers that can solve this problem!
Your quadratic is prime!

If you're trying to solve a quadratic (find x):
The factoring approach will not work for the same reasons listed above.
Try using splitting the middle or the quadratic formula instead.

Here's how you would solve it from a more advanced approach.
If you don't know what this stuff is, just ignore it.
ab = -18, a + b = -9
Find a in terms of b.
a = -9-b
Substitute this for a in the first equation.
(-9-b)b = -18
-9b-b² = -18
Multiply everything by -1 to get rid of all these negative signs.
b² + 9b = 18
Bring over that 18.
b² + 9b - 18 = 0
Apply the quadratic formula.
(a = 1, b = 9, c = -18)
$\frac{-b\pm\sqrt{b^2-4ac}}{2a}=\frac{-9\pm\sqrt{9^2-4(1)(-18)}}{1\times2}=\frac{-9\pm\sqrt{81+72}}{2}=\frac{-9\pm\sqrt{153}}{2}=\boxed{\frac{-9\pm3\sqrt{17}}{2}}$
If you need to write two distinct numbers, just write out one with a + and one with a - in place of the plus-minus sign.