Question

What two numbers add to 7 and multiply to -44

Answer 1

The numbers are 11 and -4

Explanation:

Given

Let the two numbers be
`x` and
`y`

such that:

`x + y = 7`

`x*y = -44`

Required

Find x and y

Make y the subject in:
`x + y = 7`

`y = 7 - x`

Substitute
`y = 7 - x` in
`x*y = -44`

`x(7-x) = -44`

Open bracket

`-x^2 +7x = -44`

Rewrite as:

`x^2 -7x -44=0`

Expand

`x^2 +4x-11x -44=0`

Factorize

`x(x +4)-11(x +4)=0`

Factor out x + 4

`(x -11)(x +4)=0`

Solve for x

`x =11; x =-4`

Recall that:

`y = 7 - x`

So:

`y = 7-11 = -4`

or

`y = 7--4 = 11`