Okay, fine the square roots of 100 are ±10.

There's no reason to bring the quadratic formula into this. Square roots can be negative, but when talking about the square root it's normally assumed to be the principal square root, which is the positive one.

Nope. To clarify, square roots are the opposite of squaring.

Now ask yourself:

What is 10² ?

What is (-10)² ?

If you get the same answer, then they are both the roots of the answer. +10 and -10 then gets together called ±10