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

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Answer 1 · 2015-08-19T11:15:53

$x = O/$

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.

$sqrt(x+3) color(red)(!=) -4$

What is the solution set for 2 -sqrt(x+3) =62 -sqrt(x+3) =6?