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 2018-11-16 12:24:13