First of all, you can try using the following command:
yum search libXext
After this search, you will find that you need to install the following library: libXext.i686 (or most likely libXext.i386). After that you can run:
sudo yum install libXext.i686
As an additional note, I also needed to install the following libraries for my Java application to work correctly: libXrender.i686 and libXtst.i686. I think this problem is related to the fact that we are trying to use java 32-bit version on 64-bit OS.
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