# How do you solve x^2 = x + 2 ?

Jun 26, 2016

$x = 2 \mathmr{and} x = - 1$

#### Explanation:

It is a quadratic equation, so make it equal to 0.

${x}^{2} - x - 2 = 0 \text{ factorise}$

Find factors of 2 which subtract to give 1.
As 2 is a prime number it only has factors 2 and 1.

The signs will be different, there must be more negatives.

$\left(x - 2\right) \left(x + 1\right) = 0$

If $x - 2 = 0$, then x = 2
If $x + 1 = 0$, then x = -1