Verified answer

A couple methods are reasonable:

1) Graph y=√(2s - 1) + 2 and y = s and look for where they cross.

The domain is s>=.5 and it is clear they cross at only one spot and that it has s=5.

2) Get this into a polynomial equation which can be solved by graphing.

Isolate the square root, to get √(2s - 1) = s-2

Square both sides to get 2s-1 = (s-2)^2 (this introduces extraneous root because square root must be positive!)

Solve s^2-6s+5=0 to get s=1 and s=5, but only s=5 works in original equation.

So 2s - 1 = (s - 2)^2 = s^2 - 4s + 4, so we have s^2 - 6s + 5 = 0 giving (s - 1)(s - 5) = 0

so that s = 1 or 5.Since s - 2 >0, s = 5 is the only solution.