Bug prevents windows from updating
One of the more obscure reasons why a Windows update might not be installing is because a virus or some kind of spyware is blocking it: malicious apps like these can often be squashed by Windows security updates, which is why they try and stop the latest patches from being installed on your machine.
Try running a full and thorough virus scan using whatever security software you have installed (you do have some installed, right? If you think your antivirus tool has also been compromised you can download some on-demand scanners, like this one from Microsoft or this one from Dr. Restoring key Windows files and OS options is a lot easier than it used to be, and 'resetting' Windows 10 basically means putting all the system files back to their factory state without touching your personal files along the way (although you can choose to wipe your drive completely if you want).
If Windows' own troubleshooter doesn't work (see step 4) then you can try and carry out the same process yourself manually: stopping the Windows Update service, deleting the temporary files it's created, then starting Windows Update again.This can cause issues itself, so make sure your updates definitely aren't progressing at all.In Windows 10 you can find the Windows Update page by launching the Settings app from the Start menu and clicking Update & Security – if there's something wrong and Windows knows what it is then you should find details here.Safe Mode is like a restart with extras – only the very basic apps and code that Windows needs to run are loaded into memory, so there's even less chance of a rogue, damaged file interfering with the update.In Windows 10, hold down the Shift key then choose Power and Restart from the Windows sign-in screen.