What does a subwoofer solve?

Even for "full range" floor standing speakers, the optimal placement for bass response may not be the optimal placement to produce a big soundstage and clear imaging.  For the latter, you may need to pull them out into the room and away from the walls.  Unfortunately, that probably will reduce the bass response.  A sub(s) allows you to get it back (and then some, if you like).

["purdy, I tried Velodyne they sounded good but a little pricey and they seemed very happy playing movies."]

Do recall the model of the Velodyne subwoofers you auditioned?

After a decade of not knowing who designed the pair of Phase Linear 400's that I beat the crap out of in  a PA rack and sold in working order I became a Bob Carver fan. I'm enjoying is tube mono's right now and regret not purchasing a pair of ALS's.     

If your ever in Las Vegas look me up I will demo my system for you according to Bob's Carver wife "Peggy" Bob said the following day after being at my house "Peggy" said to Bob, "Purdy's system sure sounded good you better step it up!

I love it!

Your question is “What does a subwoofer solve?”

Answer: your midrange. If you can still borrow those subs, set the XO frequency between 100 & 110.  Yes, depending upon its F3 it can extend your system’s low end and [should] improve your low end’s SQ. 

I’ll wait for the tomatoes.  
 

Tony 

I've taken a somewhat unconventional approach to bass.  I have rebuilt Maggie 3.3s and they're actively bi-amped with a Marchand crossover and Krell on top and Classe on the bottom.  Then I have two REL Britannia subs running from the Classe. 

Just this biamp-2-sub setup sounds very good.  I don't find myself "missing" bass per se.

But on Friday nights after a couple beers I prefer my stereo to sound a bit more like a club.  So I have 2 DWM woofers (match the speed of the maggies -- these are not subwoofers) and 2 more subs - another REL and a Sunfire True SuperJunior, which is both very fast and has a nice sharp thump! if you want it. 

I run the signal to this additional bass subsystem through a DBX 120X-DS, which synthesizes additional bass at one octave lower than the sample for the 4 lowest octaves in the band.  Now this would crapify the sound if I rain the Maggie 3.3s from that signal, but I don't. Instead it's the second output from the preamp into the DBX box and then to the two woofers and two subwoofers. Don't crank the volume too much or the bass is overloaded...subtlety is better. 

With this, I can have a relatively "clean" sound or one that preserves the mids and highs of the clean sound but with a thicker club sound.  The DBX can make the subs growl.