# How do you solve using the quadratic formula 2x^2 + 1 = 4x?

May 5, 2015

To use the quadratic formula we must first rearrange the quadratic equation into the form:
$a {x}^{2} + b x + c = 0$

$2 {x}^{2} + 1 = 4 x$

$2 {x}^{2} - 4 x + 1 = 0$

The quadratic formula for roots is

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

for the given example:
$x = \frac{4 \pm \sqrt{{\left(- 4\right)}^{2} - 4 \left(2\right) \left(1\right)}}{2 \left(2\right)}$

$= 1 \pm \frac{\sqrt{8}}{4}$

$= 1 \pm \frac{\sqrt{2}}{2}$

$x = 1 + \frac{1}{\sqrt{2}} \text{ or } x = 1 - \frac{1}{\sqrt{2}}$