Question

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

Answer 1

`x=2` and `x=-3`

Explanation:

In a quadratic equation `ax^2+bx+c=0`, to solve one splits the middle term in two parts so that their sum is `b` and product is `ac`.

Hence, in `x^2+x-6=0` one needs to split `1xx(-6)=-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+3x-2x-6=0` or

`x(x+3)-2(x+3)=0` or

`(x-2)(x+3)=0`

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

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