Dawnbridge

TI-84 Plus CE field manual for IB Math

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20

Solving an equation numerically

All courses

Type an equation in as it is written and let the calculator solve it. The TI-84 and Nspire return one root chosen by your starting guess, so a second pass is needed for a second root; the Casio returns the whole list.

Goal

Solve ex=5x for all real x.

1

Open the numeric solver. Press , then once, and the highlight wraps around to the solver at the bottom of the menu; press .

2

Type each side into its own box: in E1 press , then to E2 and . The solver takes the equation exactly as written, so nothing needs rearranging.

NORMALFLOATAUTOREALRADIANMP
ENTER EQUATION E1=E2
EQUATION SOLVER
E1:
ex
E2:
5x
OK
3

Select the on-screen OK option. The equation collapses to a single line above an X= row holding your starting guess and a bound row, which you can leave alone.

NORMALFLOATAUTOREALRADIANMP
EQUATION SOLVER
ex=5x
X=0
bound={-1E99,1E99}
SOLVE
4

Set the guess and solve. Type into X=, then select SOLVE. The solver replaces the row with a root, marked with a small square, and prints left-rt, the gap between the two sides at that value; 0 means it landed exactly.

NORMALFLOATAUTOREALRADIANMP
EQUATION SOLVER
ex=5x
X=0.2591711018
bound={-1E99,1E99}
left-rt=0
SOLVE
5

The solver finds one root at a time. It stops at the first root it reaches from your starting guess, and a graph of the two sides shows that they cross twice, so a guess of 0 has found only the left-hand crossing. Replace the guess with and select SOLVE again to find the other root.

NORMALFLOATAUTOREALRADIANMP
EQUATION SOLVER
ex=5x
X=2.542641358
bound={-1E99,1E99}
left-rt=0
SOLVE
Result

x=0.259 and x=2.54 to 3 s.f.

Your turn

Work each one on your calculator, then check the answer.

  1. 1

    Solve lnx=x2.

  2. 2

    Solve x3=2x.

  3. 3

    Solve cosx=x21, working in radians.