Answer
$\displaystyle \frac{-1+\sqrt{5}}{2}\approx 0.618$
$\displaystyle \frac{-1-\sqrt{5}}{2}\approx-1.618$
Work Step by Step
$p^{2}+p-1=0$
To factor the trinomial we search for
integer factors of $-1$ whose sum is $+1$ ...
... none
We can always use the quadratic formula:
(For $ax^{2}+bx+c=0,\ x=\displaystyle \frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$ )
$p=\displaystyle \frac{-1\pm\sqrt{1^{2}-4(1)(-1)}}{2(1)}$
$p=\displaystyle \frac{-1\pm\sqrt{5}}{2}$
Solutions :
$\displaystyle \frac{-1+\sqrt{5}}{2}\approx 0.618$ and
$\displaystyle \frac{-1-\sqrt{5}}{2}\approx-1.618$.
