How exactly are you planning to eradicate terrorists?
It's simple. You start by simply stating that terrorism against the United States will be met with complete and utter destruction.
This is stated right before turning Afghanistan, Iraq, Iran, and Sudan into the largest pieces of glass on the planet.
The Palestinians are told that any further conflict on the West Bank will result in the same measures.
Terrorists will care, especially if you remove "suitable" locations. Countries should understand that providing a safe haven for these animals is the same as supporting the crimes they commit. By showing that we will deal with these problems, countries will not allow enemies of the United States to hide there, and will begin to weed them out on their own.
We are the big kid on the block, and we need to start acting like it.
This group-hug-golden-light-"Can't we all just get along?" crap is exactly that: Crap. It does not work in practical application.