Question 1198789
.
<pre>

From the problem,  p^2 + p = 1,  or

    p^2 + p - 1 = 0.


Then the quadratic formula gives


    {{{p[1,2]}}} = {{{(-1 +- sqrt (1^2 + 4*1))/2}}} = {{{(-1 +- sqrt(5))/2}}}.


It provides one positive and one negative root.

We choose the positive value  

    p = {{{(-1 + sqrt(5))/2}}} = 0.618  (rounded).    <U>ANSWER</U>
</pre>

Solved.