The SOLVER

14.1How the solver works#

The solver finds a value of one variable that makes your program return zero. You write the equation as a program that ends with the quantity that should be zero, for example $x^2-2$. The program declares its variables with MVAR lines so the solver knows what to offer.

14.2Write the equation as a program#

Turn on PRGM mode with shift R/S. Press PGM.FCN (shift 3), LBL, and type a name. Then press down twice to reach MVAR and declare the variable. Type the equation in RPN with RCL for the variables, and finish with RTN. Turn PRGM off with shift R/S.

Example 14.1

Program for x squared minus 2

1. Create the program FX with one variable X. It computes X squared and subtracts 2.

   ⇧PRGMR/S⇧PGM.FCN3Σ+⇧ALPHAENTER1/xΣ+XEQ1/xENTER⇧PGM.FCN3▼▼Σ+XEQ1/xENTERRCL⇧ALPHAENTERXEQ1/xENTER⇧x²√x2−⇧PGM.FCN31/x⇧PRGMR/SEXITEXIT

2. Check the label list in the solver: FX is offered.

   ⇧SOLVER7

   

14.3Find a root#

Choose the program, then its variable. Type a guess and press the variable key to store it. Press the variable key again with no number typed to solve. The answer is in X and in the variable; Y holds the previous estimate. If no root is found the message is Extremum or Constant?. You can store two guesses (press the variable key after each) to steer toward a different root.

Example 14.2

Solve x² − 2 = 0

$$x^{2}-2=0\Rightarrow x=\sqrt2\approx1.4142$$

1. Write the program FX (see above), open the solver and pick FX, then the variable X.

   ⇧PRGMR/S⇧PGM.FCN3Σ+⇧ALPHAENTER1/xΣ+XEQ1/xENTER⇧PGM.FCN3▼▼Σ+XEQ1/xENTERRCL⇧ALPHAENTERXEQ1/xENTER⇧x²√x2−⇧PGM.FCN31/x⇧PRGMR/SEXITEXIT⇧SOLVER7Σ+Σ+

2. Type a guess of 1 and store it into X.

   1Σ+

   

3. Press X again with nothing typed to solve.

   Σ+

Example 14.3

Two guesses select the negative root

1. Store guesses −3 and −1, then solve.

   ⇧PRGMR/S⇧PGM.FCN3Σ+⇧ALPHAENTER1/xΣ+XEQ1/xENTER⇧PGM.FCN3▼▼Σ+XEQ1/xENTERRCL⇧ALPHAENTERXEQ1/xENTER⇧x²√x2−⇧PGM.FCN31/x⇧PRGMR/SEXITEXIT⇧SOLVER7Σ+Σ+3+/−Σ+1+/−Σ+Σ+

Example 14.4

Read the root afterwards

1. Solve as before, close the menus and recall the variable with all digits (DISP, FIX, 09).

   ⇧PRGMR/S⇧PGM.FCN3Σ+⇧ALPHAENTER1/xΣ+XEQ1/xENTER⇧PGM.FCN3▼▼Σ+XEQ1/xENTERRCL⇧ALPHAENTERXEQ1/xENTER⇧x²√x2−⇧PGM.FCN31/x⇧PRGMR/SEXITEXIT⇧SOLVER7Σ+1Σ+Σ+EXITEXITRCL⇧ALPHAENTERXEQ1/xENTER⇧DISPEΣ+09

See also Solve an equation with your own programSolve an equation numerically

14.4When there is no root#

Example 14.5

x squared plus 1 has no real root

1. Make a program NR that computes X squared plus 1.

   ⇧PRGMR/S⇧PGM.FCN3Σ+⇧ALPHAENTERLOGΣ+LNΣ+ENTER⇧PGM.FCN3▼▼Σ+XEQ1/xENTERRCL⇧ALPHAENTERXEQ1/xENTER⇧x²√x1+⇧PGM.FCN31/x⇧PRGMR/SEXITEXIT

2. Solve from a guess of 1.

   ⇧SOLVER7Σ+1Σ+Σ+