Question

What adds up to -54 and multiplies to -16

Answer 1

x + y = -54
xy = -16


`xy = -16`

`(xy)/(x) = \frac[-16}{x}`

`y = (-16)/(x)`


`x + y = -54`

`x + (-16)/(x) = -54`

`(x^(2))/(x) + (-16)/(x) = -54`

`(x^(2) - 16)/(x) = -54`

`x^(2) - 16 = -54x`

`x^(2) + 54x - 16 = 0`

`x = \frac{-(54) \± \sqrt{(54)^(2) - 4(1)(-16)}}{2(1)}`

`x = (-54 \± √(2916 + 64))/(2)`

`x = (-54 \± √(2980))/(2)`

`x = (-54 \± 59.6)/(2)`

`x = -27 \± 29.8`

`x = -27 + 29.8`
`or`
`x = -27 - 29.8`

`x = 2.8`
`or`
`x = 56.8`

x + y = -54
2.8 + y = -54
- 2.8 - 2.8
y = -56.8
(x, y) = (2.8, -56.8)

or

x + y = -54
-56.8 + y = -54
+ 56.8 + 56.8
y = 2.8
(x, y) = (-56.8, 2.8)

The two numbers that add up to -54 and multiply to -16 are -56.8 and 2.8.