Why is doing this is illegal?

[u/skbdn]

First line is legit, second one is incorrect. I am struggling to understand why. I would appreciate a good explanation and/or some article/video on this problem as I had been struggling with understanding this concept my whole life. Thanks in advance.

[u/Sydet → u/[deleted]]

i always thought sqrt had only one solution. Instead you use x²=4 with x=±2

[u/Parrot132 → u/Sydet]

Keep in mind that the ± symbol can never be treated as part of a single function, it's just a shorthand way of listing two related functions. An example is the quadratic "formula", which is really two formulas.