Question

What are the units on both sides of the equation: v2 = 2ax? The answer is m^2/s^2, but I wanted an explanation for why that is answer

Answer 1

You mean v^2 = 2 a x maybe ? (as in v^2 = 2 g h with g accel of gravity and h is height)
v, velocity, meters/ second so v^2 is m^2/s^2
I suspect a is acceleration, change in v / change in time = (m/s)/s = m/s^2
if x is distance that is meters, m
so a * x is m/s^2 * m = m^2.s^2
so you have m^2 /s^2on both sides