Math Help - Solving a radical equation

1. 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

2. 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 $\sqrt{2x+6}=1+\sqrt{x+4}$.

Squaring both sides, foiling and simplifying yields: $2x+6=2\sqrt{x+4}+x+5$ (Verify)

Now, get everything but the radical on the other side of the equation: $\frac{x+1}{2}=\sqrt{x+4}$.

Square both sides again to get $\tfrac{1}{4}(x^2+2x+1)=x+4 \implies x^2-2x-15=0$ (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!