Research for subwoofer

If at all possible you should go with two subs (almost all are powered BTW) as two are a huge improvement over just one for many reasons.  I’d highly recommend the SVS SB1000 Pro subs as you can get two new for only $1150, they go down to an honest 20Hz (-3dB) despite being only about 13 inches square, and they come with excellent integration software/app that’ll make it much easier to successfully dial them in properly, which is super important.  And they offer a 45-day completely risk-free trial period including shipping both ways so if for some reason they don’t work out you’re out nothing but some time, and they also offer excellent customer support if you need any help with setup, etc..  You should expect not only much better/more extended bass but also better and more solid overall imaging, dynamics, and an expanded 3D soundstage.  

https://www.svsound.com/products/sb-1000-pro-subwoofer

FYI, REL subs anywhere near this price level won’t go below the low 30Hz range so are more like additional woofers than true subwoofers, and IME although there aren’t a lot of musical instruments that go that low there’s important spatial information below 30Hz that is very meaningful and impactful especially in the areas of dynamics and an added sense of space and expanded soundstage.  Plus your speakers I believe already go down to the low 30s so there’s that.  And I agree with others the Rhytmiks are even better but will be considerably more expensive and do not come with integration software, which are not small considerations.  Just my $0.02 FWIW.  Hope this helps, and best of luck.

Like others have suggested, that’s a large area to cover, two subs will probably work best. I use two subs in each listening room. One room is 13’x9’x8’. The other is a finished basement,which is an unusual shape,roughly 25’x15’ but not a rectangle.  I have SVS subs for music. I’ve had a good experience with the SVS app.  I’ve really never heard anything negative with REL for music. HSU research is another brand worth exploring.  As suggested above,Rythmik is also highly regarded. Enjoy the hunt! 

Love my RELs  Set and forget.  Don't need remote control once set.  I did need to move them around to reduce standing waves.

What kind of budget range are you looking at?

+1 REL but, specifically, REL T9/x given the size of your room.  Compared to its peers, REL sub has lower group delay and integrates better with the main.  I have tried SVS too.