  In this paper we consider word equations with one variable (and arbitrary
many appearances of it). A recent technique of recompression, which is
applicable to general word equations, is shown to be suitable also in this
case. While in general case it is non-deterministic, it determinises in case of
one variable and the obtained running time is O(n + #_X log n), where #_X is
the number of appearances of the variable in the equation. This matches the
previously-best algorithm due to D\k{a}browski and Plandowski. Then, using a
couple of heuristics as well as more detailed time analysis the running time is
lowered to O(n) in RAM model. Unfortunately no new properties of solutions are
shown.
