# How do you solve 5x ^ { 2} + 5x - 1= 0?

Mar 12, 2017

$x = 0.171$ or $x = - 1.171$

#### Explanation:

$5 {x}^{2} + 5 x - 1 = 0$

Standard form of a quadratic equation:

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

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

$\therefore x = \frac{\left(- 5\right) \pm \sqrt{{5}^{2} - \left(4 \cdot 5 \cdot - 1\right)}}{2 \cdot 5}$

$\therefore x = \frac{- 5 \pm \sqrt{25 + 20}}{10}$

$\therefore x = \frac{- 5 + \sqrt{45}}{10}$ or $x = \frac{- 5 - \sqrt{45}}{10}$

$\therefore x = \frac{- 5 + 6.708203933}{10}$ or $x = \frac{- 5 - 6.708203933}{10}$

$\therefore x = \frac{1.708203933}{10}$ or $x = - \frac{11.708203933}{10}$

$\therefore x = 0.1708203933$ or $x = - 1.1708203933$

$\therefore x = 0.171$ or $x = - 1.171$