Answer
$\color{blue}{\left\{\dfrac{1-\sqrt5}{2}, \dfrac{1+\sqrt5}{2}\right\}}$.
Work Step by Step
RECALL:
The quadratic equation $ax^2+bx+c=0$ can be solved using the quadratic formula:
$x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$
The given equation has:
$a=1, b=-1, c=-1$
Substitute these values into the quadratic formula to obtain:
$x=\dfrac{-(-1) \pm \sqrt{(-1)^2-4(1)(-1)}}{2(1)}
\\x=\dfrac{1\pm\sqrt{1+4}}{2}
\\x=\dfrac{1\pm\sqrt{5}}{2}$
Thus, the solution set is $\color{blue}{\left\{\dfrac{1-\sqrt5}{2}, \dfrac{1+\sqrt5}{2}\right\}}$.
