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

[Dollythehun]

If it we're just a regular weed, the newspaper, black plastic sterilization would work. I'm not so sure since you have tap roots. I used to use an organic product called Burn Out. It was a cinnamon based product and it worked well. I haven't seen it for sale in awhile but, you might check online. The only problems I had were that it took two applications for perennial weeds and it "ate" my sprayers.