Playing around with the equation the solution can be written as
x = sqrt(pi+1/4)  1/2
Squaring x we see why: x^2 = pi  sqrt(pi+1/4) + 1/2 = pi  x.
Suddenly all the solutions make sense. The families of solutions are all numbers that are appropriate shifts and/or reflections of x when squared.

Posted by Jer
on 20181116 12:24:13 