Coordinate Geometry: JEE Main 2021 Mathematics question

A man starts walking from the point P($-$3, 4), touches the x-axis at R, and then turns to reach at the point Q(0, 2). The man is walking at a constant speed. If the man reaches the point Q in the minimum time, then $50\left( {{{(PR)}^2} + {{(RQ)}^2}} \right)$ is equal to ____________.