Does anybody know what this weed is that is taking over my flower beds?

[JScott]

I just moved into this house in August, and the previous owners did not care for the lawn and gardens at all. Now I have a huge flower bed in the back yard that is just filled with this invasive weed. It has a long taproot, so even though we've had a lot of rain and the ground is soft, I can't just pull it. I'm considering going full scorched earth on that flower bed and drenching it in Roundup (even though I hate Monsanto and I hate pumping chemicals into the environment. There's not a single good plant in the flower bed that i want to keep. It all needs to go and I need to just start over from nothing.

But does anybody know what this, or how i might get rid of it? I live in the DFW region of Texas (Grand Prairie, specifically), if that helps at all.