It is possible to use Newton's method for solving the above water equation, but there is a risk of converging to the wrong value of " ? "; it is important to initialise the solver to a sensible initial value, such as ( " ? max " + " ? min " ) / 2 ( which is however not sufficient : Newton's method makes no guarantees on stability ), or, alternatively, use a bracketing solver such as the bisection method or the Brent method, which are guaranteed to converge but can be slower.
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