PS: doubt on negative value of square root

[priyankur.saha]

The first few steps of a problem are shown. Finish
the problem and answer the question: what is x?

sqrt(x+3)=x−3
x+3=(x−3)^2
x+3=x2 −6x+9
0=x^2 −7x+6

Answer: x = 6 (x does NOT equal 1!)
Although this equation can be simplified and factored into
(x − 6)(x − 1)=0, you need to be careful. When you square
an equation containing a variable, you may create extraneous
solutions. Potential answers need to be plugged back in to
the original equation and verified. 6 is a genuine solution, 1 is
not.
Try plugging 1 back into the original equation to verify that x cannot
equal 1.

Why not? sqrt(4) = -2 is valid because, on GMAT, we do consider positive and negative values of square-root.
If application of negative value was wrong here, which cases such application would be correct?

[StaceyKoprince]

From The Official Guide 12th edition:

"Every positive number n has two square roots, one positive and the other negative, but SQRTn denotes the positive number whose square is 9. For example, SQRT 9 denotes 3. The two square roots of 9 are SQRT9 = 3 and -SQRT9 = -3."

Note, at the end: the negative root places the negative sign OUTSIDE of the square root sign.

I know this is confusing, but here's a way to remember it. When the test gives you SQRTx (that is, the test uses the square root symbol and does not put a negative in front of it), take the positive root only.

When the test gives you something like x^2 = 9 (that is, the test doesn't use the square root symbol), then you can solve for both 3 and -3.