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Calculus

Solve an equation numerically

Find a root of any equation by giving a starting guess and letting the calculator home in on the answer.

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Some equations have no neat formula. A numeric solver starts at your guess and improves it again and again until it lands on an answer.

The guess matters: the solver finds a root near it. If an equation has several roots, change the guess to find the others.

Classic Graphing 84

Start on the main screen: Press 2nd then mode (QUIT) to get back to the home screen. Pressing clear on a menu also backs out of it.

  1. Open the MATH menu, press the up arrow to reach the last item, the equation solver, and press enter.

    math▲enter

  2. Type the equation X² − 4 (it means X² − 4 = 0) and press enter.

    X,T,θ,nx²−4enter

  3. Type your guess 1 on the X line, then press ALPHA and enter (SOLVE).

    1alphaSOLVEenter

You should seeX=2

Classic Graphing 84 key reference

Natural Scientific 991

Start on the main screen: Press MENU, then 1 (Calculate) to return to the main calculation screen. AC clears the line you are on.

  1. Type the equation. The x key is ALPHA and the bracket key, and the = sign is ALPHA then CALC. Enter x² − 4 = 0.

    ALPHAx)x²−4ALPHA=CALC0

  2. Press SHIFT then CALC (SOLVE). It asks for a starting value: type 3 and press =.

    SHIFTSOLVECALC3=

You should seex=2

A starting value of -3 would lead to the other root, x = -2.

Natural Scientific 991 key reference

RPN Scientific 15

Start on the main screen: There is no menu to leave. Press the back arrow to clear a number you are typing, or CLx (g then back arrow) to clear the X register.

  1. The 15 solves a program. Switch to program mode with g, then R/S. Make a program that computes x² − 2 and ends with RTN: label 0 (f, SST, 0), x² (g, x²), 2, minus, and RTN (g, GSB). Switch back to run mode with g, R/S.

    gP/RR/SfLBLSST0gx²√x2−gRTNGSBgP/RR/S

  2. Key in two guesses, 1 ENTER 2, then press f, SOLVE (the ÷ key) and the label 0.

    1ENTER2fSOLVE÷0

You should seeThe square root of 2, 1.4142, is in X (and in Y).

RPN Scientific 15 key reference

RPN Advanced 42

Start on the main screen: Press EXIT (once or twice) to close any menu and return to the plain stack view of Y and X.

  1. Create a program FX that takes the variable X and returns x² − 2. This is done with the program editor: PRGM mode, LBL "FX", MVAR "X", RCL X, x², 2, minus, RTN. Then leave PRGM mode.

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

  2. Open the solver menu (SHIFT and 7), choose the program FX with the first menu key, and select the variable X.

    ⇧SOLVER7Σ+1Σ+Σ+

You should seeX=1.4142

The first menu key stores your guess 1 into X. The second press solves for X.

RPN Advanced 42 key reference

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