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

##### 1 Answer
Jul 24, 2017

See below

$x = 1.62 \mathmr{and} x = - 0.62$

#### Explanation:

The quadratic formula is $\frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

this is used for formulas $a {x}^{2} + b x + c = 0$

in your problem, $\text{ "x^2−x−1=0" }$ a=1, b=-1, c=-1#

substitute into quadratic $\text{ } \frac{- \left(- 1\right) \pm \sqrt{{\left(- 1\right)}^{2} - 4 \left(1\right) \left(- 1\right)}}{2 \cdot 1}$

this equals $\text{ } \frac{1 \pm \sqrt{1 + 4}}{2}$

$\frac{1 + \sqrt{5}}{2} \mathmr{and} \frac{1 - \sqrt{5}}{2}$

$x = 1.62 \mathmr{and} x = - 0.62$