A Tale of Three Squares

There are three squares, each with side length $a$ placed on the x-axis. The coordinates of centers of these squares are $(x_1, a/2)$, $(x_2, a/2)$ and $(x_3, a/2)$ respectively. All of them are placed with one of their sides resting on the x-axis. You are allowed to move the centers of each of these squares along the x-axis (either to the left or to the right) by a distance of at most $K$. Find