Question

What two numbers multiply to -126 and add up to -65

Answer 1

xy = -126
x + y = -65


`xy = -126`

`(xy)/(x) = (-126)/(x)`

`y = (-126)/(x)`


`x + y = -65`

`x + (-126)/(x) = -65`

`(x^(2))/(x) + (-126)/(x) = -65`

`(x^(2) - 126)/(x) = -65`

`-65x = x^(2) - 126`

`0 = x^(2) + 65x - 126`

`x = \frac{-(65) \+ \sqrt{(65)^(2) - 4(1)(-126)}}{2(1)}`

`x = (-65 \± √(4225 + 504))/(2)`

`x = (-65 \± √(4729))/(2)`

`x = (-65 \± 68.8)/(2)`

`x = (-65 + 68.8)/(2)`
`or`
`x = (-65 - 68.8)/(2)`

`x = (3.8)/(2)`
`or`
`x = (-133.8)/(2)`

`x = 1.9`
`or`
`x = -66.9`

x + y = -65
1.9 + y = -65
- 1.9 - 1.9
y = -66.9
(x, y) = (1.9, -66.9)

or

x + y = -65
-66.9 + y = -65
+ 66.9 + 66.9
y = 1.9
(x, y) = (-66.9, 1.9)

The two numbers that add up to -65 and can multiply to -126 are the numbers -66.9 and 1.9.