# How do you solve x² = 2x + 4 using the quadratic formula?

Oct 17, 2015

-1.236, 3.326

#### Explanation:

Rearrange the formula so all the terms are on one side of the equals sign. (Subtract 2x and 4 from both sides)
${x}^{2} - 2 x - 4 = 0$

The Quadratic Equation is based on the formula form of $y = a {x}^{2} + b x + c$, so now a = 2, b = -2, and c = -4

Substitute these variables into the Quadratic Equation, $x = \left(\frac{- b - \sqrt{{b}^{2} - 4 a c}}{2 a}\right)$, $\left(\frac{- b + \sqrt{{b}^{2} - 4 a c}}{2 a}\right)$

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

$x = \frac{2 - \sqrt{4 + 16}}{2} = \frac{2 - \sqrt{20}}{2} = \frac{2 - 4.472}{2}$ and

$x = \frac{2 + \sqrt{4 + 16}}{2} = \frac{2 + \sqrt{20}}{2} = \frac{2 + 4.472}{2}$

$x = - \frac{2.472}{2} , \frac{6.472}{2}$