Jap knotweed is a big problem in UK especially along river banks, but in many areas it's not too bad to deal with.
If it's in an area accessible to a tractor then it's not too difficult to eradicate. First up mow it down, dry & burn the topgrowth. For an area of 50ft X 50ft, I'd use a kybe (mattock? grubbing tool, whatever you call them over there!) to lift the woody rootballs & burn those too. Then when the underground rhizomes start to throw up new shoots, let them get a leaf or two & spray with glyphosate. You'll have to do this over at least two full growing seasons, but it will work. Just mowing, or just spraying won't work.
The best way to do it though on such a small area is to pen some weaner pigs on the patch. They'll eat all the topgrowth, root up & eat all the juicy rhizomes & leave the woody rootballs, so you can just pick them up & burn them. Once the pigs are moved, spray any regrowth, which should be minimal. I successfully got rid of a patch of Jap Knotweed in one field using this method &, without spraying at all, I've had no regrowth in twenty odd years.