Question

What two numbers multiply to get -36 and add to get 9

Answer 1

xy = -36
x + y = 9


`xy = -36`

`(xy)/(x) =(-36)/(x)`

`y = (-36)/(x)`


`x + y = 9`

`x + (-36)/(x) = 9`

`(x^(2))/(x) + (-36)/(x) = 9`

`(x^(2) - 36)/(x) = 9`

`9x = x^(2) - 36`

`0 = x^(2) - 9x - 36`

`x = \frac{-(-9) \± \sqrt{(-9)^(2) - 4(1)(-36)}}{2(1)}`

`x = (9 \± √(81 + 144))/(2)`

`x = (9 \± √(225))/(2)`

`x = (9 \± 15)/(2)`

`x = (9 + 15)/(2)`
`or`
`x = (9 - 15)/(2)`

`x = (24)/(2)`
`or`
`x = (-6)/(2)`

`x = 12`
`or`
`x = -3`

x + y = 9 or x + y = 9
12 + y = 9 or -3 + y = 9
- 12 - 12 + 3 + 3
y = -3 or y = 12
(x, y) = (12, -3) or (x, y) = (-3, 12)

The two numbers that add up to 9 and multiply to -36 are the numbers -3 and 12.