xy = -216
x + y = 6
x + y = 6
x - x + y = -x + 6
y = -x + 6
xy = -216
x(-x + 6) = -216
x(-x) + x(6) = -216
-x² + 6x = -216
-x² + 6x + 216 = 0
-1(x²) - 1(-6x) - 1(216) = 0
-1(x² - 6x - 216) = 0
-1 -1
x² - 6x - 216 = 0
x² - 18x + 12x - 216 = 0
x(x) - x(18) + 12(x) - 12(18) = 0
x(x - 18) + 12(x - 18) = 0
(x + 12)(x - 18) = 0
x + 12 = 0 or x - 18 = 0
- 12 - 12 + 18 + 18
x = -12 or x = 18
x + y = 6 x + y = 6
-12 + y = 6 18 + y = 6
+ 12 + 12 - 18 - 18
y = 18 y = -12
(x, y) = (-12, 18) or (x, y) = (18, -12)
The two numbers that multiply to -216 and add up to 6 are -12 and 18.
