# How do you solve x^2-2x+7=-4 using the quadratic formula?

Nov 11, 2016

$x = 1 \pm i \sqrt{10}$

(There are no real solutions.)

#### Explanation:

Make one side equal to zero by adding 4 to each side:
${x}^{2} - 2 x + 7 = - 4$
${x}^{2} - 2 x + 11 = 0$

$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$
$x = \frac{2 \pm \sqrt{{\left(- 2\right)}^{2} - \left(4\right) \left(1\right) \left(11\right)}}{2 \cdot 1}$
$x = \frac{2 \pm \sqrt{- 40}}{2}$
$x = \frac{2 \pm 2 i \sqrt{10}}{2}$
$x = 1 \pm i \sqrt{10}$