One way to test the validity of a formula is to look at the units. I believe the definitions for energy and force still hold in relativity. I am having trouble formatting the square operation for Fluther. In the equations below, interpret a 2 by a symbol as being the square.
Energy = force x distance = (mass x acceleration) x distance.
Lett m stand for mass, d for distance and t for time. Acceleration = velocity/t = (d/t)/t) = d/t^2.
Substituting, we get energy = m d/ t2 x d = m d2/t^2.
Now let’s check the units in E = mc2 = m(d/t)2 = m d2/t2. The units match, so the formula passes this test. The formula would definitely be invalid without squaring c.