if you want both domains to show the same site, you should add the one you bought as a parked domain through cPanel (Parked domains always point to the web root). This way the free subdomain you signed up with remains your main domain and both work essentially the same as far as a visitor sees.
You need to configure the domain at go daddy to point to our servers, the easiest way of doing this is setting the name servers for the domain to: ns1.x10hosting.com and ns2.x10hosting.com
Please note that it may take up to 48 hours before the domain has propagated and fully works after making such changes.