What number multiply to be 110 but add up to be -21?

Let x be the first nuber and y be the second...so..

x + y = -21  and x * y = 110

Using the first equation, let y = -21-x   and substituting this into the second equation, we have

x(-21 -x) = 110    simplifying this, we have

-21x - x² = 110   and rearranging, we have

x² + 21x + 110 = 0      factor this

(x + 11) (x +10) = 0 

So x either equals -11 and y = -10    or   x = -10 and y = -11 ....  both solutions are valid....