Show all of your work to solve each equation and to check for extraneous solutions:

[SQRT(x)]=-2

I already solved it as:

x=-2

(x)2=(-2)2

X=4

but my teacher sent it back to me with ''When you are checking solutions, you only simplify each side of the equation.You should not add, subtract, multiply, divide, or square both sides of the equation.I asked you to explain why the correct answer is "no solution".''

So I tried again by writing the equation as:

x=-2

x=-2: No solution for x and r

x=-2

f(x) cannot be negative for x and r

No solution for x and r

and my teacher wrote back to me again stating: ''I'm not following your explanation.What do you mean by x and r?Show how you substitute 4 for x in x=-2.Then simplify the left side of the equation to see if the two sides of the equation match.If they do, x=4 is a solution.If they do not, x=4 is extraneous and we would have no solution.''

I do not understand what she wants me to do, nor what I am doing wrong.

Please help me with this equation, thank you very much.