I am trying to figure out what this weed is, also I am location in West Michigan near the lake if the climate will also help determine what this is.

{{gwi:1349568}}

{{gwi:1349570}}

{{gwi:1349572}}

I'm pretty sure that it isn't mare's tail. I believe that the one on the right is mare's tail and the one on the left is the mystery weed and are clearly not the same.

{{gwi:1349574}}

Also if it helps for identifying the plant here is a picture of the roots.

{{gwi:1349576}}

I also noticed some purple coloring in the roots seen very clearly here.

{{gwi:1349577}}

Any sort of information on identifying this weed would be greatly appreciated, thanks in advance for any help that can be provided.