Answer
$x=\left\{ \dfrac{1-\sqrt{5}}{2},\dfrac{1+\sqrt{5}}{2}\right\}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given equation, $
x^2-x-1=0
,$ use the Quadratic Formula.
$\bf{\text{Solution Details:}}$
In the equation above, $a=
1
,$ $b=
-1
,$ and $c=
-1
.$ Using the Quadratic Formula which is given by $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a},$ then
\begin{array}{l}\require{cancel}
x=\dfrac{-(-1)\pm\sqrt{(-1)^2-4(-1)(-1)}}{2(1)}
\\\\
x=\dfrac{1\pm\sqrt{1+4}}{2}
\\\\
x=\dfrac{1\pm\sqrt{5}}{2}
.\end{array}
The solutions are $
x=\left\{ \dfrac{1-\sqrt{5}}{2},\dfrac{1+\sqrt{5}}{2}\right\}
.$
