HP 35s HP 35s scientific calculator - User Guide - Page 129
Understanding and Controlling SOLVE, Verifying the Result
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value Stores 4 in E ;prompts for F. Stores 11 in F and calculates x and y. value of y Understanding and Controlling SOLVE SOLVE first attempts to solve the equation directly for the unknown variable. If the attempt fails, SOLVE changes to an iterative (repetitive) procedure. The procedure starts by evaluating the equation using two initial guesses for the unknown variable. Based on the results with those two guesses, SOLVE generates another, better guess. Through successive iterations, SOLVE finds a value for the unknown that makes the value of the equation equal to zero. When SOLVE evaluates an equation, it does it the same way does - any "=" in the equation is treated as a " - ". For example, the Ideal Gas Law equation is evaluated as P × V - (N × R × T). This ensures that an equality or assignment equation balances at the root, and that an expression equation equals zero at the root. Some equations are more difficult to solve than others. In some cases, you need to enter initial guesses in order to find a solution. (See "Choosing Initial Guesses for SOLVE," below.) If SOLVE is unable to find a solution, the calculator displays See appendix D for more information about how SOLVE works. Verifying the Result After the SOLVE calculation ends, you can verify that the result is indeed a solution of the equation by reviewing the values left in the stack: The X-register (press to clear the viewed variable) contains the solution (root) for the unknown; that is, the value that makes the evaluation of the equation equal to zero. Solving Equations 7-7