# How do you solve x^2 -3x = -7 using the quadratic formula?

Jul 20, 2015

$x = \frac{3 + \sqrt{19} i}{2} , \frac{3 - \sqrt{19} i}{2}$

#### Explanation:

${x}^{2} - 3 x = - 7$

Get all terms on the left side.

${x}^{2} - 3 x + 7 = 0$ is a quadratic equation in the form $a {x}^{2} + b x + c = 0$, where $a = 1 , b = - 3 , \mathmr{and} c = 7$.

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

Substitute known values into the formula.

$x = \frac{- \left(- 3\right) \pm \sqrt{- {3}^{2} - 4 \cdot 1 \cdot 7}}{2 \cdot 1}$ =

$x = \frac{3 \pm \sqrt{9 - 28}}{2}$

$x = \frac{3 \pm \sqrt{- 19}}{2}$

$x = \frac{3 \pm \sqrt{19} i}{2}$

Solve for $x$.

$x = \frac{3 + \sqrt{19} i}{2}$

$x = \frac{3 - \sqrt{19} i}{2}$