How does one solve?

This is actually a two part question. First, you can't really divide both sides by , since it could be negative (or even zero).

I figure we can do this problem by separating it into three cases. First, let and see if it is a solution (it is). Then let and .

When , then . Then we can take the square root of both sides and get . If we interpret that as and then write it as or , we have the correct full answer. But why is that the correct interpretation? How does someone explain that to his daughter?

Last case is to let . Then and . Using the same logic as last paragraph, that would indicate that , or that , which is wrong.

What's the correct way to solve?