xy = -100
x + y = 21
x + y = 21
x - x + y = -x + 21
y = -x + 21
xy = -100
x(-x + 21) = -100
x(-x) + x(21) = -100
-x² + 21x = -100
-x² + 21x + 100 = 0
-1(x²) - 1(-21x) - 1(-100) = 0
-1(x² - 21x - 100) = 0
-1 -1
x² - 21x - 100 = 0
x² - 25x + 4x - 100 = 0
x(x) - x(25) + 4(x) - 4(25) = 0
x(x - 25) + 4(x - 25) = 0
(x + 4)(x - 25) = 0
x + 4 = 0 or x - 25 = 0
- 4 - 4 + 25 + 25
x = -4 or x = 25
x + y = 21 or x + y = 21
-4 + y = 21 or 25 + y = 21
+ 4 + 4 - 25 - 25
y = 25 or y = -4
(x, y) = (-4, 25) or (x, y) = (25, -4)
The two numbers that multiply to -100 and add up to 21 are 25 and -4.
Solution Set: {-4, 25}
