Why did the United States use atomic weapons during World War II?

The United States used atomic weapons to end the Second World War. Japan was relentless in their efforts and from the outside looking in, there was no sign of them surrendering. The United States realized the only way to stop them was to drop atomic bombs on Nagasaki and Hiroshima.
The usage of atomic bombs was also to exemplify the power the United States held. This power would launch the U.S. into international fame. As many would expect, it did. It also created a competition. After the events that took place in August of 1945, nations like the Soviet Union, Germany and so on were immediately intrigued and wanted to be able to combat such a weapon.
Overall, the use of the atomic weaponry was solely to end the war and show off essentially. Roosevelt believed this would provide a shield and invincibility for the United States but unfortunately it just catapulted the world into a Cold War.

The United States used atomic weapons seek an end to World War II without invading Japan. The invasion of Japan, code-named X-Day, was projected to cost over one million American casualties. It would also make the war potentially last another two years. All of this was based on numbers generated by the War Department after seeing the difficulties of taking Iwo Jima and Okinawa. Although some Americans were not concerned about this, there was also the consideration that the Japanese would fight to the last man and that an invasion of Japan would lead to a near-extermination of the inhabitants of the country. The War Department did not take into account that American submarines had been wreaking havoc on the Japanese merchant marine and that such an invasion might not even be necessary; Japan was close to collapse when the atomic bombs were dropped in August 1945.
Truman also decided to drop the atomic bombs with an eye towards the future. The Soviet Union, an ally in the war, currently occupied Eastern Europe through either direct occupation or the establishment of puppet governments. The United States did not want the Soviet Union dictating the peace in Japan in a shared occupation; therefore, the United States moved swiftly to ensure that it was the leader in the Japanese peace movement. It was also hoped that putting the atomic weapons on display would intimidate the Soviets.