To add to Tinstaafl's comments:
the simple theory has a number of assumptions which simply are not correct for simple aeroplanes
eg a simple drag polar with no power effects etc
a constant power output & propeller efficiency, or constant THP (thrust horse-power), which is far from true for a fixed pitch propeller
If anyone is interested there's a detailed
performance analysis of the 172 online here.
(there is an error there too, I see!)