Question

What multiplies to -12 but added together equals -10

Answer 1

Let the two numbers be x and y, then,
xy = -12 . . . (1)
x + y = -10 . . . (2)
From (2), x = -10 - y . . . (3)
Putting (3) into (1), gives
(-10 - y)y = -12
-10y - y^2 = -12
y^2 + 10y - 12 = 0
$y= \frac{-10\pm \sqrt{10^2-(4\times(-12))} }{2} = \frac{-10\pm \sqrt{148} }{2} = \frac{-10\pm 2\sqrt{37} }{2} = -5\pm\sqrt{37}$

Therefore, the two numbers are $-5+\sqrt{37}$ and $-5-\sqrt{37}$