Answer
$x= 4$
Work Step by Step
Given equation-
$\sqrt {2x+1} +1$ = $x$
i.e. $\sqrt {2x+1} -x +1$ = $0$
We are asked to find all real solutions of this equation.
Graphing $y$ = $\sqrt {2x+1} -x +1$, using graphing calculator-
There is only one $x-intercept$, i.e. $x= 4$
Therefore $x= 4$
