Question

How do you solve `x^2-x=6`?

Answer 1

Set the trinomial equal to zero and factor into two binomials .

`x= 3 and x = -2`

Explanation:

`x^2 -x -6 = 6-6` This gives

`x^2 -x -6 = 0`

The C value is negative this means one of the binomials must be negative and the other positive.
The B value is negative this means that the negative value is larger than the positive value.
The coefficient of the B is 1 This means that the two factors have a difference of 1

Factors of 6 are `6xx1 and 2xx3`

2 and 3 have a difference of 1 so these are the factors that work
The 3 must be negative because it is larger and the 2 positive so

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

Set each factor equal to zero and solve for each of the binomials to find the possible values for x.

`x - 3 = 0` add 3 to both sides

`x -3 +3 = 0 +3`

`x = 3`

`x +2 = 0` subtract 2 from both sides

`x +2 -2 = 0 -2` this gives

`x = -2`