What are two numbers that multiply to - 20 and add up to 1?

xy = - 20

x + y = 1

x + y = 1

x - x + y = - x + 1

y = - x + 1

xy = - 20

x (-x + 1) = - 20

x (-x) + x (1) = - 20

-x² + x = 20

-x² + x + 20 = 0

-1 (x²) - 1 (-x) - 1 (-20) = 0

-1 (x² - x - 20) = 0

-1 - 1

x² - x - 20 = 0

x = - (-1) ± √ ((-1) ² - 4 (1) (-20))

2 (1)

x = 1 ± √ (1 + 80)

2

x = 1 ± √ (81)

2

x = 1 ± 9

2

x = 0.5 ± 4.5

x = 0.5 + 4.5 or x = 0.5 - 4.5

x = 5 or x = - 4

x + y = 1

5 + y = 1

- 5 - 5

y = - 4

(x, y) = (5, - 4)

or

x + y = 1

-4 + y = 1

+ 4 + 4

y = 5

(x, y) = (-4, 5)

The two numbers that add up to 1 and multiply to - 20 are - 4 and 5.