Answer
{$-\dfrac{1}{2} - \dfrac{\sqrt{5}}{2},-\dfrac{1}{2} + \dfrac{\sqrt{5}}{2}$}
Work Step by Step
Given: $x^2+x-1=0$
This can be re-written as: $x^2+x=-1$
We will have to add both sides $(\dfrac{1}{2})^2$ to complete the square.
Thus, $x^2+x+(\dfrac{1}{2})^2=-1+(\dfrac{1}{2})^2$
or, $(x+\dfrac{1}{2})^2=\dfrac{5}{4}$
or, $(x+\dfrac{1}{2})=\pm\sqrt{\dfrac{5}{4}}$
or, $x=-\dfrac{1}{2} \pm \dfrac{\sqrt{5}}{2}$
Hence, our desired solution set is {$-\dfrac{1}{2} - \dfrac{\sqrt{5}}{2},-\dfrac{1}{2} + \dfrac{\sqrt{5}}{2}$}
