Question

What adds up to -7 but multiplies to 10

Answer 1

x + y = -7
xy = 10


`xy = -7`

`(xy)/(x) = (-7)/(x)`

`y = (-7)/(x)`


`x + y = -7`

`x + (-7)/(x) = -7`

`(x^(2))/(x) + (-7)/(x) = 7`

`(x^(2) - 7)/(x) = -7`

`x^(2) - 7 = -7x`

`x^(2) + 7x - 7 = 0`

`x = \frac{-(7) \± \sqrt{(7)^(2) - 4(1)(-7)}}{2(1)}`

`x = (-7 \± √(49 + 28))/(2)`

`x = (-7 \± √(77))/(2)`

`x = (-7 \± 8.8)/(2)`

`x = (-7 + 8.8)/(2)`
`or`
`x = (-7 - 8.8)/(2)`

`x = (1.8)/(2)`
`or`
`x = (-15.8)/(2)`

`x = 0.9`
`or`
`x = -7.9`

x + y = -7
0.9 + y = -7
- 0.9 - 0.9
y = -7.9
(x, y) = (0.9, -7.9)

or

x + y = -7
-7.9 + y = -7
+ 7.9 + 7.9
y = 0.9
(x, y) = (-7.9, 0.9)

The two numbers that add up to -7 and multiply to -10 are -7.9 and 0.9.