Why did truman finally used the atomic bomb?

At the time the american public was in support of using the bomb and truman felt like he had few other choices about how to act quickly against japan in order to keep the war in the pacific from escalating. As far as the U. S. could tell Japan had every intention of fighting to the death and was willing to risk anything to win, so the "special bomb" were a solution to prevent even greater world travesty.