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Windows 7 and Linux on the same PC-error when installing Win7 SP1
If you have Linux and Win 7 installed on the same machine and run across an install error when trying to install Win 7 SP1, then this one is for you.
Pay attention to the the last paragraph of the article and use Disk Management to solve your problem.
Windows 7/2008 R2 Service Pack 1 fails with 0x800f0a12 - The Servicing Guy - Site Home - TechNet Blogs