Question

How do you solve `x^2 + 7x - 44 = 0`?

Answer 1

`x = -11, 4`

Explanation:

Begin with writing the equation into brackets.

`(x + a)(x + b) = 0`

You want to find `a` and `b` such that `a + b = 7` and `a * b = -44`.

Through a process of trial and error, this gives `a = -4` and `b = 11`.

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

Anything multiplied by `0` is `0`, meaning at least one of the brackets has to be equal to `0`. This actually gives two answers for `x`. Set each one equal to zero and then solve.

`x - 4 = 0`
`x = 4`

or

`x + 11 = 0`
`x = -11`