Two solutions for you to try. One is officially provided by Microsoft and the other is provided by this community of posters.
I just searched for "fix windows update" in bing/google and it lead me to an official Microsoft site where I was able to download the latest windows troubleshooter. After running it and applying fixes, one of my computers restarted and applied the updates
successfully. This should be the first thing you try. Here's a direct link: https://support.microsoft.com/en-us/help/10164/fix-windows-update-errors
If the above solution doesn't work, you can try the community provided fix which many people have reported as working. It's down below for your convenience. I recommend you run all of these commands in the order provided.
open CMD as administrator
- How To: Click the Start button, type cmd, right click on cmd and choose "run as administrator"
- Type or copy these lines into the cmd window and hit enter for each one:
SC config wuauserv start= auto
SC config bits start= auto
SC config cryptsvc start= auto
SC config trustedinstaller start= auto
P.S. Microsoft: Lock these threads and post official answers to the questions so people don't have to guess at what the best and most viable solution is.