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 \( 50\big((PR)^2 + (RQ)^2\big) \) is equal to:
