Why the CAPS????
It makes posts VERY difficult to read.... and presuming you want people to read and answer your posts, why make it harder than it has to be to read it - especially posts of some length...!?!?!?
Anyways....
Putting foam or blankets/padding do ABSOLUTELY NOTHING to stop sound from escaping.... they are used to control sound reflections.......
You are confusing sound absorption and sound isolation - two very different goals.
To isolate sound to a given room/space/whatever requires mass... essentially constructing a room within a room... of course this is relatively expensive.... and there's also no half-assed way to get around it if you want effective isolation. The physical laws of sound transmission don't give a crap about someone's budget!
If you have a problem with excess reflectivity, room modes, resonances - then you can use sound absorption materials to tame some reflections and errant frequencies in the room. This you CAN do on a budget, but will not do anything to assist sound isolation.