What is the solution set for #2 -sqrt(x+3) =6#?
As it is written, this equation has no solution among real numbers, and here's why that is the case.
For real numbers, you can only take the square root of a positive number, and the result will always be another positive number.
#color(blue)(sqrt(x) >=0", "(AA)x in [0, + oo))#
Rearrange the equation to isolate the square root on one side
#-sqrt(x+3) = 4#
#sqrt(x+3) = -4#
Since the square root must always be a positive number, your equation does not have a valid solution among real numbers.
#sqrt(x+3) color(red)(!=) -4#