Answer
$x=4$
Work Step by Step
$\sqrt{2x+1}+1=x$
Take the $1$ to substract to the right side of the equation:
$\sqrt{2x+1}=x-1$
Let's square both sides of the equation:
$(\sqrt{2x+1})^{2}=(x-1)^{2}$
$2x+1=x^{2}-2x+1$
Take all terms to the right side of the equation:
$x^{2}-2x+1-2x-1=0$
Simplify:
$x^{2}-4x=0$
Take out common factor $x$:
$x(x-4)=0$
We get two solutions, which are:
$x=0$ and $x=4$
Let's check our answers:
With $x=0$:
$\sqrt{2(0)+1}+1=0$
$2\ne0$ False
With $x=4$
$\sqrt{2(4)+1}+1=4$
$4=4$ True
So, our answer is $x=4$
