Consider the following attempt to solve the equation $4 x \sqrt { 2 x - 1 } = 10 x - 5$ :
$$\begin{aligned}
4 x \sqrt { 2 x - 1 } & = 10 x - 5 \\
4 x \sqrt { 2 x - 1 } & = 5 ( 2 x - 1 ) \\
16 x ^ { 2 } ( 2 x - 1 ) & = 25 ( 2 x - 1 ) ^ { 2 } \\
16 x ^ { 2 } & = 25 ( 2 x - 1 ) \\
16 x ^ { 2 } - 50 x + 25 & = 0 \\
( 8 x - 5 ) ( 2 x - 5 ) & = 0
\end{aligned}$$
The solutions of the original equation are $x = \frac { 5 } { 8 }$ and $x = \frac { 5 } { 2 }$.
Which one of the following is true?