But a = b does imply a2 = b2, which is what Cornstalks seems to be denying. His insistence on the distinction between squaring the sides of the equation or squaring terms makes no sense in the particular case, because there is only one term on each side of the equal sign.
I'm saying what you're really doing when you square both sides is multiply both sides by themselves. So when you have the equation:
-7 = √x
You can't just square the terms and come up with
49 = x
You have to square both sides, which is effectively multiplying each side by itself:
(-7)2 = (√x)2
Or, another way of writing this is:
49 = √x√x
If you don't square the sides you skip a step and assume that √x√x = √(xx) = x, which isn't generally true.
That's what I'm arguing.