What two numbers add to 15 and multiply to negative 312?

X + y = 15

xy = - 312

x + y = 15

x - x + y = - x + 15

y = - x + 15

xy = - 312

x (-x + 15) = - 312

x (-x) + x (15) = - 312

-x² + 15x = - 312

-x² + 15x + 312 = 0

-1 (x²) - 1 (-15x) - 1 (312) = 0

-1 (x² - 15x + 312) = 0

-1 - 1

x² - 15x + 312 = 0

x = - (-15) ± √ ((-15) ² - 4 (1) (312))

2 (1)

x = 15 ± √ (225 - 1248)

2

x = 15 ± √ (-1023)

2

x = 15 ± 31.984i

2

x = 7.5 ± 15.992

x = 7.5 + 15.992 or x = 7.5 - 15.992

x = 23.492 or x = - 8.492

x + y = 15

23.492 + y = 15

- 23.492 - 23.492

y = - 8.492

(x, y) = (23.492, - 8.492)

or

x + y = 15

-8.492 + y = 15

+ 8.492 + 8.492

y = 23.492

(x, y) = (-8.492, 23.492)

The two numbers that add up to 15 and mutliply to - 312 are - 8.492 and 23.492.