If you look in the user manual on the vizio site for your soundbar, it references a *wired* subwoofer as an option. Unless there's something very incomplete about each product's published specifications, your unit does not have the internal components to be able to send a signal out to such a (proprietary) sub.
If possible, think about a true AV receiver w/ proper surrounds/sub. Plan 'B' would be a HTIB scenario.
I have a vizio SB3820-C6 2.0 sound bar for my TV. I want to add a subwoofer. I have found a replacement subwoofer for a Vizio SB3831-C6M 3.1 Would this subwoofer be compatible with my soundbar?

Chowhound
Comic Vine
GameFAQs
GameSpot
Giant Bomb
TechRepublic