insulating existing finished basement

Hello all, I purchased a home a year ago. Half the basement id finished and is used as a rec room. I had to cut a hole in the drywall to investigate a pipe. I noticed that there is no insulation iside the dry wall and basement walls. I'd like to refinish all of the basement and and wonder if i should i try to insulate them? If so, can i use the blow-in insulation or am i screwed? Any other options? kudos steve
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