Have you had this problem? A carpet that came rolled up and never really wanted to lie flat after? The carpet's great for keeping the dirt from the entry door at bay but the corner drove us nuts as we kept tripping on it. That black thingy in the background is Bonus having a mid morning snack in the kitchen btw.
We tried wetting the corner and putting heavy weights on it but that didn't help so in the end I got my trusted velcro out. The sticky back version.
I just stuck the female part of the velcro to the corner of the carpet and the male to the corresponding spot on the floor. The easiest way to make sure it's the right spot on the floor is by actually sticking them to each other and then peeling off the backing on the male (how weird does this sound to you?) and laying the corner in place. That way they correspond perfectly.
Walk on top to make sure it's stuck down well. If the carpet needs removing to clean the floor just tear the velcro apart. You'll have to clean around the strip on the floor of course but I prefer that to constantly tripping.
And there it is flat as a pancake!