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# 9.2. Solving Nonlinear Equations Iteratively

## Problem

You'd like to solve a nonlinear equation that requires an iterative solution and are not sure how to approach it in Excel.

## Solution

Use Goal Seek or Solver. See the introduction to this chapter for more information on how these two tools differ as well as their respective advantages and disadvantages.

## Discussion

In this recipe, I want to show you by way of example how to use Excel's built-in Solver and Goal Seek tools to solve a nonlinear equation. The equation we'll consider is:

This equation is used to estimate a frictional drag coefficient, C f , as a function of the Reynolds number , R N , for some ship resistance calculations. There are other equations for this same purpose but I chose this classical one because it can't be written in an explicit form of y = g(x). Instead, you have to resort to some iterative method to find a value of C f corresponding to some given value of R N .

I'll show you how to use both Goal Seek and Solver to solve this example problem. In both cases the equation must first be rearranged in the following form:

Now we can use Solver or Goal Seek to iteratively find a value for C f given a value for R N that makes the righthand side of this equation equal to 0. But first, you need to enter the righthand ...

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