# How do you solve 5x^2 - 2x – 2 = 0?

Aug 12, 2015

The solutions are:

color(blue)(x= (1+sqrt11)/5

color(blue)(x= (1-sqrt11)/5

#### Explanation:

5x^2−2x – 2=0

The equation is of the form color(blue)(ax^2+bx+c=0 where:
$a = 5 , b = - 2 , c = - 2$

The Discriminant is given by:

color(blue)(Delta=b^2-4*a*c

$= \left(- {2}^{2}\right) - \left(4 \cdot 5 \cdot \left(- 2\right)\right)$

$= 4 + 40$

$= 44$

The solutions are found using the formula:

color(blue)(x=(-b+-sqrtDelta)/(2*a)

$x = \frac{- \left(- 2\right) \pm \sqrt{44}}{2 \cdot 5} = \frac{2 \pm 2 \sqrt{11}}{10}$

$= \frac{\cancel{2} \left(1 \pm \sqrt{11}\right)}{\cancel{10}} = \frac{1 \pm \sqrt{11}}{5}$

The solutions are:

color(blue)(x= (1+sqrt11)/5

color(blue)(x= (1-sqrt11)/5