No, it's not a binary solution. It's going to take everything, diplomatic, economic, military, cyber, progressive ideals, trampling basic freedoms we have here on them, religious, and psychological propaganda to put this cat back in the bag. The military solution is but one small but necessary piece. Realistically, all it's doing is making the fight on their turf as opposed to ours. Put the folks trained and willing to do it in harm's way as a willing target. This isn't going to end for decades. I doubt we see an end in our lifetime. Not unless we get medevil and commit religious persecution and genocide. Even then, I don't know if that would do it.
This will be a never ending war because we are fighting an ideal that is in direct opposition to the western way of life. The two cannot coexist and we can't hide from it and pretend it doesn't exist. From Morocco to the Philippines, we're at war. Hell, we're at war internally at home as they are dumping billions of dollars into "progressive ideals" in order to try and normalize their behavior and create sympathetic ears back here. This war started decades before we acknowledged it formally. There will never be piece without tremendous loss on both sides. On ours, the loss will be our morality, on theirs it will be in flesh.
Once 9/11 happened, Pandora's box of evil opened up. There will be no peaceful solution as we drag a culture kicking and screaming a millennia forward into progressive equality. It will take the pressure from the entire modern world and the moderate Muslims to commit horrendous attrocities to stop it. I don't know if the common understanding and idea of victory is achievable. Beating ISIS back into splintered cells is only a small piece. It's a military victory, but it will have minimal impact.