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Collision Detection Help

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I'm programming a 2D sidescroller/platformer written on Java using Slick2D. The past couple weeks, I've had a lot of trouble with collision detection/response.

Detection & Response I'm Looking For
Rectangle-on-rectangle collision detection, with the response being to move the involved sprites away from each other. If one or both sprites are defined as static (represented by isStatic), don't move that sprite.

Here's my code relating to it in my Sprite class:

The Problem
My problem is when either sprite in the collision is not perfectly square. How could I modify this code to work with non-square rectangles?
If I'm way off course with this code, if someone else has better, working code, I'd accept that too.

Thanks in advance!
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