1) Log into the Sharing API as an Administrator through https://machine.domain.com:7443/arcgis/sharing/rest
2) In your account information page, there will be an Org ID property with a link to 0123456789ABCDEF. Click on that link
3) All the way at the bottom, click on Servers under the Child Resources section
4) Click on the Server ID link and then Update Server
5) Enter the new services URL and the existing Admin URL and click Update.
You'll then need to go through everyone's content and update any URLs to any services that are not hosted services
1) Go into a users content in the Sharing API, (https://machine.domain.com:7443/arcgis/sharing/rest/content/users/<user>/items/ for example)
2) Select a non-hosted service and at the bottom, select Update Item
3) Enter the new URL in the URL parameter box
You can use the Python API to traverse through each user and their content, find all non-hosted services and update the URLs if you want. You'll need to republish hosted services for the URL to update.