Question

What two numbers multiply to -112 and add up to -54

Answer 1

-56 and 2.

-56 x 2 = -112

-56 + 2 = -54

I found this out by first dividing -112 by two, and then figuring out what number that I should add to it to equal -54 :) Hope this helps!

Answer 2

xy = -112
x + y = -54


`xy = -112`

`(xy)/(x) = (-112)/(x)`

`y = (-112)/(x)`


`x + y = -54`

`x + (-112)/(x) = -54`

`(x^(2))/(x) + (-112)/(x) = -54`

`(x^(2) - 112)/(x) = -54`

`x^(2) - 112 = -54x`

`x^(2) + 54x - 112 = 0`

`x^(2) + 56x - 2x - 112 = 0`

`x(x) + x(56) - 2(x) - 2(56) = 0`

`x(x + 56) - 2(x + 56) = 0`

`(x - 2)(x + 56) = 0`

`x - 2 = 0`
`or`
`x + 56 = 0`

`x = 2`
`or`
`x = -56`

x + y = -54
2 + y = -54
- 2 - 2
y = -56
(x, y) = (2, -56)

or

x + y = -54
-56 + y = -54
+ 56 + 56
y = 2
(x, y) = (-56, 2)

The two numbers that multiply to -12 and add up to -54 are -56 and 2.