How was the question of New Mexico's eastern boundary finally settled?

During the 1846 Mexican-American War, the U. S. provisional government of New Mexico was established. But during this time the boundaries of the new state was ambiguous.

During the 1850s, a new boundary proposal was made prohibiting slavery. This request was approved and simultaneously the territory of Utah was created in the north. But finally the boundaries of New Mexico were set by the Compromise of 1850. The United States Congress in September of the same year established officially the New Mexico territory and the Utah territory.