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

Mar 24, 2018

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

$x = 3 \mathmr{and} x = - 2$

#### 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 $6 \times 1 \mathmr{and} 2 \times 3$

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

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

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

$x = - 2$