Solve the equation for x. Identify any extraneous solutions.

Question

anonymous · Answer

$$q=\sqrt{-7q}$$

mathmale · Answer

Which problem would you like help with?  Please, post only 1 question at a time.

anonymous · Answer

This one! ^^^^

mathmale · Answer

Your posting has the variable q, whereas your instructions say to "solve for x."

Please clarify this situation.

anonymous · Answer

But thats what the question says

anonymous · Answer

attachment

mathmale · Answer

Well, then I'm going to assume that we're solving for q, not for x.

I'm going to work with you on a similar problem; you could then apply what you've learned to solve the question you've posted.

We'll try to solve the following for x:
$$x=\sqrt{-3x}$$

mathmale · Answer

First, I'd remove the radical (the square root).  How?

anonymous · Answer

I dont know

mathmale · Answer

Square both sides.  type the results.

mathmale · Answer

$$(x)^{2}=(\sqrt{-3x})^{2}$$
becomes

x^2 ("x squared") = -3x

x^2=-3x
$$x ^{2}=-3x$$

mathmale · Answer

This is a quadratic equation.  We want to put it into standard form.  Thus, we add 3x to both sides, and end up with 
$$x ^{2}+3x=0$$
Next, we factor this, and get

mathmale · Answer

x(x+3)=0.
Setting each of the 2 factors equal to zero,
we get

x=0 and x=-3

You must check each of these possible solutions in the original equation.  I suspect that one of them will be a solution and the other will not; the one that is not a solution is your "extraneous root."