Answer
$x=-\dfrac{1}{2}\pm\dfrac{\sqrt{5}}{2}$
Work Step by Step
Using the completing the square method, then,
\begin{array}{l}
x^2+x-1=0\\
x^2+x=1\\
x^2+x+\left( \dfrac{1}{2} \right)^2=1+\left( \dfrac{1}{2}\right)^2\\
x^2+x+\dfrac{1}{4}=1+\dfrac{1}{4}\\
\left( x+\dfrac{1}{2} \right)^2=\dfrac{5}{4}\\
x+\dfrac{1}{2}=\pm\sqrt{\dfrac{5}{4}}\\
x=-\dfrac{1}{2}\pm\dfrac{\sqrt{5}}{2}
.\end{array}
