What multiplies to - 900 and adds to 5?

Xy = - 900

x + y = 5

x + y = 5

x - x + y = - x + 5

y = - x + 5

xy = - 900

x (-x + 5) = - 900

x (-x) + x (5) = - 900

-x² + 5x = - 900

-x² + 5x + 900 = 0

-1 (x²) - 1 (-5x) - 1 (-900) = 0

-1 (x² - 5x - 900) = 0

-1 - 1

x² - 5x - 900 = 0

x = - (-5) ± √ ((-5) ² - 4 (1) (-900))

2 (1)

x = 5 ± √ (25 + 3600)

2

x = 5 ± √ (3625)

2

x = 5 ± 5√ (145)

2

x = 2.5 ± 2.5√ (145)

x + y = 5

2.5 ± 2.5 √ (145) + y = 5

- (2.5 ± 2.5√ (145) - (2.5 ± 2.5√ (145)

y = 2.5 ± 2.5√ (145)

(x, y) = (2.5 ± 2.5√ (145), 2.5 ± 2.5√ (145))

The two numbers that add up to 5 and multiply to - 900 are 2.5 ± 2.5√ (145).