Question

What is the solution set for `2 -sqrt(x+3) =6`?

Answer 1

`x = O/`

Explanation:

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`