Let $f$ be a real valued function defined for all real numbers $x$ such that for some positive constant $a$, the equation $f\left(x+a\right)=\frac{1}{2}+\sqrt{f\left(x\right)-{\left(f\left(x\right)\right)}^2}$ holds for all $x$. Then $f\left(x\right)$ is periodic function with period equal to