# How do you factor and solve 3x^2 – x – 1 = 0?

Jun 3, 2017

$x = \text{either " 0.3837959396 " / } \frac{1 + \sqrt{13}}{12}$

$\mathmr{and} = - 0.217129273 \text{ / } \frac{1 - \sqrt{13}}{12}$

#### Explanation:

We can use the quadratic formula to solve this.

$3 {x}^{2} - x - 1 = 0$

$a {x}^{2} + b x + c = 0$

$a = 3$
$b = - 1$
$c = - 1$

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

$x = \frac{- \left(- 1\right) \pm \sqrt{- {1}^{2} - 4 \times 3 \times - 1}}{2 \times 6}$

$x = \frac{1 \pm \sqrt{1 - 12 \times - 1}}{2 \times 6}$

$x = \frac{1 \pm \sqrt{1 - - 12}}{12}$

$x = \frac{1 \pm \sqrt{13}}{12}$

$x = \frac{1 \pm 3.605551275}{12}$

${x}_{1} = \frac{1 + 3.605551275}{12}$

${x}_{1} = \frac{4.605551275}{12}$

color(blue)( x_1 = 0.3837959396 or (1 + sqrt13) / 12

${x}_{2} = \frac{1 - 3.605551275}{12}$

${x}_{2} = - \frac{2.605551275}{12}$

color(blue)( x_2 = -0.217129273 or (1 - sqrt13) / 12