Ive been trying to get adsense on my site but I can't because of the domain name so google won't approve my application for adsense. because the domain iis a subdomain of x10. Is there any way around this without having to buy a domain name?
That sounds like it would be a restriction by Google rather then by us.
If Google won't approve the application due to the domain, I'd assume you need a third party domain for it to work, there are free domain providers out there that might work if you don't want to actually buy one.
There's a few..
If you're going to use dot.tk or anything similar (especially other services from Freenom) then you should be aware that on free domains they will grab your domain if you have a LOT of users or / and requests, and they will accept any report against your domain (false or not).
So, if you do decide to take the free domain route then you may need to be aware of that. When you do get enough money out of AdSense, I would recommend getting a premium domain to avoid such troubles and help gain more.