What two numbers can be multiplied to be - 150 and added to be 5

Xy = - 150

x + y = 5

x + y = 5

x - x + y = - x + 5

y = - x + 5

xy = - 150

x (-x + 5) = - 150

x (-x) + x (5) = - 150

-x² + 5x = - 150

-x² + 5x + 150 = 0

-1 (x²) - 1 (-5x) - 1 (-150) = 0

-1 (x² - 5x - 150) = 0

-1 - 1

x² - 5x - 150 = 0

x = - (-5) ± √ ((-5) ² - 4 (1) (-150))

2 (1)

x = 5 ± √ (25 + 600)

2

x = 5 ± √ (625)

2

x = 5 ± 25

2

x = 2.5 ± 12.5

x = 2.5 + 12.5 or x = 2.5 - 12.5

x = 15 or x = - 10

x + y = 5

15 + y = 5

- 15 - 15

y = - 10

(x, y) = (15, - 10)

or

x + y = 5

-10 + y = 5

+ 10 + 10

y = 15

(x, y) = (-10, 15)

The two numbers that add up to 5 and multiply to - 150 are 15 and - 10.