How to solve $x = \arccos(x)$

Question

How does one solve $$ x = \arccos(x) $$ for $x$?

Is there an exact solution achievable by hand? I tried wolfram|alpha, but it only spits out the solution $$ x = \text{ root of }\quad x-\cos^{-1}(x) \quad \text{ near } x = 0.739085 $$

Answer 1

There is no solution to this equation in terms of elementary functions. However, one can still use numerical methods to solve it (which is probably how Wolfram|Alpha generates the solution).