here is the process to "push" a system app to your phone.
1. download the ROM or GAPPS that hangouts originally came from to your sdcard or extsdcard if you don't already have it
2. using root explorer or es file explorer, navigate to system/app in the rom or GAPPS zip file and extract hangouts.apk
3. copy or move hangouts.apk into system/app on your phone
4. change permissions to -rw-r--r--
5. reboot and it should work fine