Im attempting to set up my projector & speakers in my living room, & having a little trouble. The only stud near the ideal spot puts the image 4 inches from a corner wall. My speakers are the Ascend 340's which are 7.5 inches wide & ported. My general assumption is that the speaker needs to be around 1 foot away from the corner, is that correct? Or could i get away with a closer distance?
The only solution i have found so far is to point the projector 1-2 inches to the right to move it out of the corner. How bad am i affecting image quality?

You image will not be square. The right side will be taller than the left side, and most projectors do not correct that kind of keystoning.

You don't absolutely need to anchor to a stud, there are very good anchor bolts and anchoring hardware that will easily support the low weight of your pj. Alternatively, you could anchor your pj to a sheet of material that in turn is large enough to be anchored to studs for that extra feeling of confidence!