How to Solve Nonlinear Equations in Excel (with Easy Steps)

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There are many ways to solve different types of equations in Excel. But to solve the nonlinear equations, we had to use the Solver Add-in of Excel. This add-in doesnâ€™t remain pre-enabled in Excel, needs to be enabled from the Excel Options. In this article, weâ€™ll show how to activate it and how to use it to solve nonlinear equations in Excel.

What Is a Nonlinear Equation?

For an equation, when the change of the output doesnâ€™t get proportional to the change of the input and if the equation appears as a curved line in the graph, then it is called a Nonlinear equation or quadratic equation.

Now, by following some easy steps, weâ€™ll solve the two nonlinear equations given below.

Step 1: Inserting Nonlinear Equation

First, weâ€™ll have to insert the left side of the equations in two cells using the cell reference of the variables. But remember, weâ€™ll have to consider the equation by keeping the right side zero.

Steps:

• For the first equation, insert the following formula in Cell B9â€“
`=D9^2+D10^2-25`
• Then hit the ENTER button to finish.

• And for the second equation, insert this formula in Cell B10â€“
`=D10-D9^2`

Step 2: Creating Objective Equation to Solve Nonlinear Equation

For using the Solver Add-in, we need an objective equation. So, weâ€™ll sum the two cells where we inserted the left side of the equation to use it as an objective equation.

Steps:

`=SUM(B9:B10)`

Step 3: Activating Solver Add-in to SolveÂ Nonlinear Equation

The input process is done, now weâ€™ll enable the Solver Add-in. If you have enabled it already or know how to do it, then skip this step.

Steps:

• Click on the File tab first.

• Next, select Options from the appeared menu.

• Finally, mark Solver Add-in and press OK.

Step 4: Inserting Objective and Variable Cells in the Solver Add-in

Now see, the Solver Add-in is available in the Analyze section of the Data ribbon.

Steps:

• Click as follows to open it: Data > Solver.

Soon after you will get a window of Solver Add-in like the image below

The first action is to set the objective equation and variable cells.

• Click on the upside arrow button from the Set Objective box as shown above and an input box will open up.
• Select Cell D12 and hit ENTER.

• After that, mark the Value Of option and insert 0 in the value box.
• Next, click on the upside arrow button from the By Changing Variable Cells

• Select the cells of variables and press ENTER.

Step 5: Enter Cell Reference and Constraint to Solve Nonlinear Equation

Here, weâ€™ll insert the cell reference of the left side of the nonlinear quadratic equations and the constraints.

Steps:

• Click on the Add button.

• Insert Cell B9 in the Cell Reference box for the first equation.

• Then choose = from the drop-down box and insert 0 in the Constraints box.
• Next, press OK.

• Following the same way, insert the cell reference and constraints for the second equation.

The Solver add-in can extract the solutions with a detailed answer report. Also, there are other options too, you can choose your most convenient one.

Steps:

• Mark the Make Unconstrained Variables Non-Negative
• And then just press the Solve button.

• After a few moments, a dialog box will appear like this. Mark the Keep Solver Solution option and select Answer from the Reports section.
• Finally, just press OK.

Here are our calculator variables.

The solverÂ will show you the answer report in a new sheet like the image below.

Things to Remember

• To solve nonlinear equations, you must have to set an objective equation.
• Donâ€™t forget to mark the Make Unconstrained Variables Non-Negative
• GRG Nonlinear should be selected by default as the solving method, if not you need to adjust that.

You can download the free Excel workbook from here and practice independently.

Conclusion

Thatâ€™s all for the article. I hope the procedures described above will be good enough to solve nonlinear equations in Excel. Feel free to ask any questions in the comment section, and please give me feedback.

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1. x and y are switched in your solution. x is actually 4.524938 and y is 2.12719