# Equation Solve - fx-991ES PLUS - Casio Calculator Tutorials

Solving equations is possible with the equation solver in the fx-991ES PLUS calculator's

functionality. Once the equation has been entered, the calculator uses the Newton-Raphson numerical method to solve the equation. Because the equation solver uses a numerical method, it only works with equations with a single variable.**shift-solve**

For example, I will solve the following equation for \(x\).

$$\large{\frac{x^2-6}{x+3} = 10}$$

- Begin by entering the left expression normally, using \(\color{maroon}{\fbox{X}}\) for the variable that you wish to solve.
- Use \(\color{maroon}{\fbox{=}}\) (accessible through \(\color{maroon}{\fbox{ALPHA}}\ \fbox{CALC}\)), then enter the right expression.
*shift-solve*to enter equation solve by pressing \(\color{#A80}{\fbox{SHIFT}}\ \fbox{CALC}\). \(\text{Solve for X}\) will be shown on screen.- If applicable, enter a number as the starting point for the Newton-Raphson numerical method solving for \(x\). The current value of \(X\) is displayed for reference and will be used if no new value is provided.
- Press \(\fbox{=}\) to begin solving the equation.

The first value of \(x\) as found by the numerical method will be provided on the screen and is saved to the \(X\) variable. The difference between the left expression and the right expression is shown as the solution to \(L-R\).

Caveats: As mentioned, this only works with equations with one variable. The variable can be used multiple times, as shown in this example, however you can't use two or more variables such as \(x\) and \(y\). If you wish to use more than one variable, you need to use the quadratic equation solve. Furthermore, the Newton-Raphson numerical method only returns one value. To find another value, change the start point at step 4. For example, if there are two solutions, one positive and one negative, and you find the positive one, enter a negative number for the start point to find the negative answer.