Why does
(2-X)^2=-1
have no real solution?
But that's not to say that doing that wouldn't work...
$\displaystyle (2 - x)^2 = -1$
$\displaystyle 4 - 4x + x^2 = -1$
$\displaystyle x^2 - 4x + 5 = 0$
Now checking the discriminant gives...
$\displaystyle \Delta = (-4)^2 - 4\times 1\times 5$
$\displaystyle = 16 - 20$
$\displaystyle = -4 < 0$.
So no solution exists.
Having said that - you are right, it IS easiest to just notice that you can not square any real number to get a negative result.