# How do you solve x^2 – 3x – 1 = 0 using the quadratic formula?

May 31, 2017

Using the quadratic formula, $x$ can either $= - 2.618 \mathmr{and} - 0.382$

#### Explanation:

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

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

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

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

$x = \frac{- 3 \pm \sqrt{{3}^{2} - 4 \times 1 \times - 1}}{2 \times 1}$

$x = \frac{- 3 \pm \sqrt{9 - 4}}{2}$

$x = \frac{- 3 \pm \sqrt{5}}{2}$

$x = \frac{- 3 \pm 2.236}{2}$

${x}_{1} = \frac{- 3 - 2.236}{2}$

${x}_{1} = \frac{- 5.236}{2}$

color(blue)(x_1 = -2.618

${x}_{2} = \frac{- 3 + 2.236}{2}$

${x}_{2} = \frac{- 0.764}{2}$

color(blue)(x_2 = -0.382