Moto x powering off/app optimization

My sister and nephew were having the same issue and I cleared cache for them, both are fine now. They had the constant optimizing apps and that stopped it. It's a good thing to do any time your phone starts acting stupid

Here are the instructions, give it a try and see if that helps, it really should.

edit: Clearing cache will not wipe any data or change any settings, no worries doing it.
another edit: It does take a while so let it do it's thing.

 

The only other thing I can think of would be a factory reset. Be sure to save all your data/photos etc. first.