Implied plus-minus sign in radical equation? Say we have: $$\sqrt{x+7}=5-x$$
Is it implicitly understood that the following also holds? $$-\sqrt{x+7}=5-x$$
I'm exploring the notion of "extraneous solutions." In this example, solving either equation leads to two results, namely x=2 and x=9. 
Standard practice is to check these solutions once they're found by plugging them into the original equation. Thus, x=2 is shown to be the right answer, assuming we're using the first equation above. Meaning, x=9 is extraneous.
But really, x=9 is the solution to the second equation.
What's the right way to think about the square root operator given this discussion? Does the second equation logically follow from the first and, if so, is it right to call the second equation's solution "extraneous?"

If what you say is true, then we should be able to add both sides,
$$\sqrt{x+7}-\sqrt{x+7}=5-x+5-x$$
$$0=2(5-x)$$
$$\implies x=5$$
Going back, this is not true in either equation.
