# How do you solve x^2 - 6x + 2 = 0 using the quadratic formula?

Mar 10, 2016

$x = 3 \pm \sqrt{7}$

#### Explanation:

color(blue)(x^2-6x+2=0

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

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

Where

color(red)(a=1,b=-6,c=2

Substitute the values in the formula

$\rightarrow x = \frac{- \left(- 6\right) \pm \sqrt{- {6}^{2} - 4 \left(1\right) \left(2\right)}}{2 \left(1\right)}$

$\rightarrow x = \frac{6 \pm \sqrt{36 - 8}}{2}$

$\rightarrow x = \frac{6 \pm \sqrt{28}}{2}$

$\rightarrow x = \frac{6 \pm \sqrt{4 \cdot 7}}{2}$

$\rightarrow x = \frac{6 \pm 2 \sqrt{7}}{2}$

$\rightarrow x = \frac{\cancel{6} \pm \cancel{2} \sqrt{7}}{\cancel{2}}$

rArrcolor(green)(x=3+-sqrt7