$\displaystyle \begin{array}{{>{\displaystyle}l}} \sqrt{2x+1} -2\sqrt{x} +1=0\ \\ DK\ :\begin{cases} x\geqslant -\frac{1}{2} & \\ x\geqslant 0 & \end{cases}\rightarrow x\geqslant 0\\ 2x+1=( 4x-1)^{2}\\ 2x+1=16x^{2} -8x+1\\ \rightarrow 16x^{2} -10x=0\\ \rightarrow 2x( 8x-5) =0\\ \rightarrow \left[ \begin{array}{l l} x=0 & \\ 8x-5=0 & \end{array} \right.\rightarrow \left[ \begin{array}{l l} x=0 & \\ x=\frac{5}{8} & \end{array} \right. \end{array}$
