Recently I have been solving a electrostatics questions where you are given two charges and want to find where the third charge should be kept so that net force on it is 0. It generates a quadratic equations which can be solved and correct answer could be choosed intuitively. But when I saw its solution, the quadratic was solved by taking square root both sides.
My question is how can we exactly know where we can take square root both side to solve a quadratic and where we can't?
You can always take the square root on both sides as long as the terms are nonnegative, e.g. $$ x^2=4\ \Rightarrow \ \sqrt{x^2} =\sqrt 4.$$ What you can not do is claim that $\sqrt{x^2}=x$, since $x$ may be negative!