# How do you solve 4x² - 4x – 1 = 0?

Mar 21, 2016

$x = \frac{1 + \sqrt{2}}{2}$

#### Explanation:

color(blue)(4x^2-4x-1=0

This is a Quadratic equation (in form $a {x}^{2} + b x + c = 0$)

color(brown)(x=(-b+-sqrt(b^2-4ac))/(2a)

Where

color(red)(a=4,b=-4,c=-1

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

$\rightarrow x = \frac{4 \pm \sqrt{- {4}^{2} - 4 \left(4\right) \left(- 1\right)}}{8}$

$\rightarrow x = \frac{4 \pm \sqrt{16 - \left(- 16\right)}}{8}$

$\rightarrow x = \frac{4 \pm \sqrt{16 + 16}}{8}$

$\rightarrow x = \frac{4 \pm \sqrt{32}}{8}$

$\rightarrow x = \frac{4 \pm \sqrt{16 \cdot 2}}{8}$

$\rightarrow x = \frac{4 \pm 4 \sqrt{2}}{8}$

$\rightarrow x = \frac{{\cancel{4}}^{1} \pm {\cancel{4}}^{1} \sqrt{2}}{\cancel{8}} ^ 2$

color(green)(rArrx=(1+-sqrt2)/(2)