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

May 31, 2017

$x = \frac{3 \pm \sqrt{- 3}}{2} = \frac{3}{2} \pm \frac{1}{2} i \sqrt{3}$

#### Explanation:

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

the quadratic equation needs to be in the following form:

$a {x}^{2} + b x + c = 0$

where a, b and c is any number.

Finally, we plug the values in the formula and solve for $x$.

Step 1: Get the equation in the right format:

${x}^{2} - 3 x + 3 = 0$

$a = 1$
$b = - 3$
$c = 3$

Step 2: Plug the values into the quadratic formula:

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

$x = \frac{3 \pm \sqrt{9 - 12}}{2}$

$x = \frac{3 \pm \sqrt{- 3}}{2} = \frac{3}{2} \pm \frac{1}{2} i \sqrt{3}$

There are no real roots to this quadratic - instead there are two imaginary roots.