Second-Order Linear Equations · Superchallenge problem

A continuous function $f$ satisfies $f(x) + 2\displaystyle\int_0^x f(s)\,ds + 5\int_0^x (x - s)\,f(s)\,ds = 1$ for all real $x$. Find the smallest positive $x$ with $f(x) = 0$, rounded to four decimal places.