What numbers multiply to 6 and add up to 9

Xy = 6

x + y = 9

x + y = 9

x - x + y = - x + 9

y = - x + 9

xy = 6

x (-x + 9) = 6

x (-x) + x (9) = 6

-x² + 9x = 6

-x² + 9x - 6 = 0

-1 (x²) - 1 (-9x) - 1 (6) = 0

-1 (x² - 9x + 6) = 0

-1 - 1

x² - 9x + 6 = 0

x = - (-9) ± √ ((-9) ² - 4 (1) (6))

2 (1)

x = 9 ± √ (81 - 24)

2

x = 9 ± √ (57)

2

x = 4.5 ± 0.5√ (57)

x + y = 9

4.5 ± 0.5√ (57) + y = 9

- (4.5 ± 0.5√ (57)) - (4.5 ± 0.5√ (57))

y = 4.5 ± 0.5√ (57)

(x, y) = (4.5 ± 0.5√ (57), 4.5 ± 0.5√ (57))

The two numbers that multiply to 6 and add up to 9 are 4.5 ± 0.5√ (57).