Question

What two numbers add to 7 and multiply to -44

Answer 1

Answer:

The numbers are 11 and -4

Step-by-step 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

$y = 7--4 = 11$