2 numbers that multiplied give me -21 and added -22
Let x, y be the numbers
So
xy = -21 (1)
x + y = -22 → y = -22 - x (2)
Subbing (2) into (1), we have that
x ( -22 - x) = -21 simplify
-22x - x^2 = -21 add 21 to both sides
22x + x^2 = 21 subtract 21 from both sides
22x + x^2 - 21 = 0 rearrange
x^2 + 22x - 21 = 0
We can use the quadratic formula to solve this
WoframAlpha gives the two solutions for x as :
-11 + √142 and -11 - √142
Choosing either for x will mean that y will be the other solution