.zipx files is a new advanced compression technology used by a popular archiving software called WinZip. Zipx files offer much better compression than the traditional zip compression and compresses files to make them much smaller.
In order to open .zipx files you will need to download and install a trial version of WinZip, PowerArchiver or Stuffit Deluxe.
All of these softwares are paid, however you can install WinZip and continue using it for free for a long time. Please note you will have to download WinZip 12 or higher in order to open .zipx files.