Which event convinced president truman to drop the atomic bomb?

There are a couple of events that led to the President Truman's verdict to drop the atomic bomb:

1) Japanese leaders failed to heed the warnings and surrender.

2) Japanese belief that they were the 'chosen' people, and would fight to the death to allow the Japanese 'Empire' to continue to survive.

3) Operation Downfall, Olympic, & Overlord proved to be costly and had a high chance of having large amount of casualties.

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for this case we have the following equation:

we apply distributive property to the terms within parentheses.

subtracting 2 on both sides of the equation:

president thomas jefferson hoped that the embargo act of 1807 would the united states by demonstrating to britain and france their dependence on american goods, convincing them to respect american neutrality and stop impressing american seamen. instead, the act had a devastating effect on american trade.