How do you know which route to pick?

GMATHacks - 10 sample questions

Walker - At what point did you decide to test the question itself? Was it when you saw that setting up one equation in two different ways, only one gets you to the answer? I need to learn how to think outside of box. Thanks

Yeah, I found it.
So, there is no typo in your post but as I said there is no x that satisfies the equation. (GMAT doesn't deal with complex numbers).

When I decided to test the question? Hm... I often "play" with numbers before solving a problem. Sometimes it helps to find a shortcut.
Let's forget about this particular question. I guess I got what your problem is.

Suppose we have the equation: a = b. Can we say that a^2 = b^2? Yeah, it's correct. Now, let's take a look at an example:

\(-\sqrt{x} = 2\)
\((-\sqrt{x})^2 = 2^2\)
\(x = 4\)

Is it right? No. Because \(-\sqrt{4} = -2 \neq 2\). So, a solution of a^2=b^2 isn't necessarily a solution of a = b and it's important to check it out. So, x=4 is a correct solution of \((-\sqrt{x})^2 = 2^2\) but it's not a solution of \(-\sqrt{x} = 2\).

Hope it helps

Wait....you mentioned that -\(\sqrt{4}\)= -2 but since you can interpret -\(\sqrt{4}\) as (-1) * \(\sqrt{4}\) = (-1) * [either(-2) or 2] and therefore -\(\sqrt{4}\) = actually either 2 or (-2). No?

https://en.wikipedia.org/wiki/Square_root

"Every positive number x has two square roots. One of them is \(\sqrt{x}\), which is positive, and the other \(-\sqrt{x}\), which is negative."
"Every non-negative real number x has a unique non-negative square root, called the principal square root, denoted by a radical sign as \(\sqrt{x}\).

\(\sqrt{x}\) is the principal square root and non-negative. So \(-\sqrt{4}\) means only -2 because a radical sign means only non-negative square root.