Thread: Solving a radical equation

I am not too sure on how to actually solve this radical equation been stuck on it for a while the equation is:

\sqrt{2x+6} - \sqrt{x+4} =1

any help would be awesome
thanks in advance

Originally Posted by DjNito

I am not too sure on how to actually solve this radical equation been stuck on it for a while the equation is:

\sqrt{2x+6} - \sqrt{x+4} =1

any help would be awesome
thanks in advance

I would first rewrite it as .

Squaring both sides, foiling and simplifying yields: (Verify)

Now, get everything but the radical on the other side of the equation: .

Square both sides again to get (Verify)

Now solve this quadratic equation for x to get two possible answers. Then test for possible extraneous solutions by plugging them into the original equation.

I hope this helps!