Re-partitioning Time Machine Drive for use as Windows backup as well

I recently bought a 1TB external drive to use primarily as a backup for my apple laptop. I plugged the disk into my laptop and it asked me if I wanted to use it as my time machine backup device, I said I did indeed.

Since the backup drive is quite a bit bigger than my laptop hard drive, I tried to reformat it, shrinking the time machine partition to match the size of my laptop drive, and formatting the other as FAT32. I did this in OSX (or maybe in Ubuntu), so I could backup my Windows desktop onto it as well. But the desktop doesn't recognize the disk, presumably since it was partitioned with a non-Windows partition table.

So is there any way to use the external drive as both a time machine backup drive on one partition, and as windows backup on another partition? If I completely reformat the disk in Windows can I do this? I'd prefer not to have to backup all the data off the disk again, but if I need to, I can.

Thanks in advance.

formatted as FAT32.... that looks like your problem right there.
It should be formatted as NTFS.

The issue is that Windows doesn't recognize the drive, and I know it can recognize FAT32 partitions, because pretty much every flash drive comes with one FAT32 partition. So I'm just wondering if the issue IS, in fact, the Apple partition table, and if I could just wipe the drive and write a windows partition table but still use it as my time machine drive. Anyone?

BTW, I am pretty sure Apple OS can't write to NTFS.

I recently bought a 1TB external drive to use primarily as a backup for my apple laptop.