x + y = 39
xy = -880
x + y = 39
x - x + y = -x + 39
y = -x + 39
xy = -880
x(-x + 39) = -880
x(-x) + x(39) = -880
-x² + 39x = -880
-x² + 39x + 880 = 0
-1(x²) - 1(-39x) - 1(-880) = 0
-1(x² - 39x - 880) = 0
-1 -1
x² - 39x - 880 = 0
x² - 55x + 16x - 880 = 0
x(x) - x(55) + 16(x) - 16(55) = 0
x(x - 55) + 16(x - 55) = 0
(x + 16)(x - 55) = 0
x + 16 = 0 or x - 55 = 0
- 16 - 16 + 55 + 55
x = -16 or x = 55
x + y = 39
-16 + y = 39
+ 16 + 16
y = 55
(x, y) = (-16, 55)
or
x + y = 39
55 + y = 39
- 55 - 55
y = -16
(x, y) = (55, -16)
The two numbers that add up to 39 and multiply to -880 are 55 and -16.
