Solve rad2x+1=2x-5

Question

Solve rad2x+1=2x-5

anonymous · Answer

$$\sqrt{2x+1}=2x-5$$

larseighner · Answer

$$ \large \sqrt{2x+1}=2x-5$$

$$ \large \sqrt{2x+1}-2x+5 = 0$$

$$ \large -\sqrt{2x+1}+2x-5 = 0$$

$$ \large 2x -\sqrt{2x+1}-5 = 0$$

$$ \large (2x+1) -\sqrt{2x+1}-6 = 0$$

$$ \large (\sqrt{2x+1} - 3)(\sqrt{2x+1}+2) = 0$$

larseighner · Answer

$$\large (\sqrt{2x+1} - 3)=0 $$
$$\large \sqrt{2x+1} =3 $$
$$\large 2x+1=9 $$
$$\large x=4 $$


$$\large(\sqrt{2x+1}+2) = 0$$
$$\large \sqrt{2x+1}=-2$$
root is imaginary, isn't it? Check this.

larseighner · Answer

@zepdrix @dumbcow  What have I done here?  The 4 is a solution.

dumbcow · Answer

yes you are correct, solution is x=4

btw nice technique with the factoring, usually just square both sides with these types of equations

larseighner · Answer

Thank you. I have an odd way of looking at things.

larseighner · Answer

Here is a plot of what is actually going on.  The red part is what you do NOT have.  That would be your equation with a minus sign on the radical.  The blue part is what you DO have. And as you can see, 4 is the only root of the blue part.