Why did settlers expand westward despite the challenges of the physical environment there?

The correct answer to this open question is the following.

Settlers expanded westward despite the challenges of the physical environment there because they were hoping for a better life.

After the Louisiana Purchase of 1803, President Thomas Jefferson ordered the Lewis and Clark Expedition that lasted two years in order to explore the new territories before allowing the westward expansion. So people started to move west and had to cross the Oregon Trail that represented a risk. Many people die trying to cross it. The road was long and implied the cost of movement wagons, livestock, and personal belongings.

i think it is the byzantine empire