If you tap screen on the battery usage page, how many hours and minutes are reported?
Anyway, it seems maybe some system processes are draining battery heavily, so, you can shutdown the phone, wait one or two minutes, then power on again.
Occasionally, the battery level is not properly reported. You may check this guide (it was written for Moto X, but it also applies to Moto X): http://motoxhub.com/how-to-solve-battery-life-problem-of-moto-x-after-kitkat-android-4-4-update/
Of course, if none of these works, you may ask the local service centre to check the hardware.