# How do you factor and solve x^2+x-6=0?

Aug 1, 2016

$x = 2$ and $x = - 3$

#### Explanation:

In a quadratic equation $a {x}^{2} + b x + c = 0$, to solve one splits the middle term in two parts so that their sum is $b$ and product is $a c$.

Hence, in ${x}^{2} + x - 6 = 0$ one needs to split $1 \times \left(- 6\right) = - 6$ in two parts whose sum is $1$. It is apparent that these are $3$ and $- 2$, hence ${x}^{2} + x - 6 = 0$ can be written as

${x}^{2} + 3 x - 2 x - 6 = 0$ or

$x \left(x + 3\right) - 2 \left(x + 3\right) = 0$ or

$\left(x - 2\right) \left(x + 3\right) = 0$

i.e. either $x - 2 = 0$ i.e. $x = 2$

or $x + 3 = 0$ i.e. $x = - 3$