# How do you solve x^2 -x = 5x - 9?

Jul 10, 2015

$x = 3$

#### Explanation:

${x}^{2} - x = 5 x - 9$

Subtract $5 x$ from both sides of the equation.

${x}^{2} - x - 5 x = - 9$ =

${x}^{2} - 6 x = - 9$

Add $9$ to both sides.

${x}^{2} - 6 x + 9 = 0$

We now have a quadratic equation with the form $a {x}^{2} + b x + c = 0$, where a=1; b=-6; and $c = 9$.

We can solve for $x$ using the quadratic formula.

$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$ =

$x = \frac{- \left(- 6\right) \pm \sqrt{- {6}^{2} - 4 \cdot 1 \cdot 9}}{2 \cdot 1}$ =

$x = \frac{6 \pm \sqrt{36 - 36}}{2}$ =

$x = \frac{6 \pm \sqrt{0}}{2}$ =

$x = \frac{6 \pm 0}{2}$ =

$x = \frac{6}{2}$ =

$x = 3$