Thanks all, very helpful!
10x10 is being generous for the room size. It's just a small sitting/TV room, probably more like 7x9.
I'm pretty sure the TV has a headphone jack.
So if I get this, I just plug it into the headphone jack, plug the AC connector to the wall for power, and it's good to go? Volume will be adjusted automatically with the TV remote?
https://www.amazon.com/SHARKK-Computer-Speakers-Multimedia-Bluetooth/dp/B01AIIGO6C/ref=sr_1_1?s=pc&ie=UTF8&qid=1478491572&sr=1-1-spons&keywords=computer+speakers&psc=1