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You are correct so far. The values of x are 5 and 13.
But take note that in radical equations, after solving for the values of x, it is necessary to plug-in these values to the original equation. Since there are instances that the solved values don't work on the original equation.
So let's plug-in x=5 to check.
Since the resulting condition is True, then x=5 is a solution to the equation.
Next, plug-in x=13 to check too.
`18=8 ` (False)
Notice that left side does not simplify to 8. So, x=13 is not a solution to the given equation.
Therefore, the solution to `x+sqrt(2x-1)=8` is `x=5` only.