2008 LTZ Max Towing Capacity

[2008 Tahoe Eric]

So my 2008 Chevy Tahoe says the LTZ with towing is at a max 8200 lbs. I recently purchased a travel trailer that's about 7700 lbs. empty. I know leaving 500 lbs. isn't the greatest, but what cushion do I have, if any, when they designed the towing torque?