What two numbers multiply to - 100 but add up to 21

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}