If you're using analogue output (the Green, Orange, and Black 3.5mm jacks), then you can just plug in a pair of speakers into the Gray jack on the computer and position them to the right and left.
Here are the jacks on an 8-channel (7.1) computer system:
And here are where the speakers go:
If you already have a 5.1 system, it will plug into the Green (Front Left/Front Right), Orange (Center/Subwoofer), and Black (Surround Back Left/Surround Back Right) jacks. You should be just fine plugging another speaker system into the Gray port (Surround Left/Surround Right) and positioning the speakers to create a 7.1 system. The re is no inherent sound quality loss with doing this, but you'll have to do more work to balance all the speakers manually since you're working with two separate speaker systems with their own volume controls.
New image added as my preferred speaker layout as a sound engineer. From SounDoctor which has a very nice article on the subject - including a stronger reinforcing of my idea that adding 2 more speakers is often more trouble than it's worth ;-)
What would you use to decode the signals for the additional two channels? – fixer1234 – 2015-01-08T15:48:20.540
I'd say a) yes, but b) why bother? How many sources of true 7.1 do you actually use with any regularity. Also c) Fixing the phase offsets/time delays of 7.1 is not an easy task & will only ever really work in a large room [read:Cinema] or if you never move your head, even if you get it right. & I guess d) how well-matched are this new pair? Will they complement or just detract from the original, matched, setup. – Tetsujin – 2015-01-08T21:02:57.230