How to Use the TI-Calculator Solver

Many physics problems consist of solving a mathematical equation. If a simple equation reduces to one unknown variable, the calculator is often used to perform the math that finds the solution.

Example: 7t2 - 5t = 0
To solve for t, rearrange the equation... 7t2 = 5t
...divide both sides by 7t... (7t2)/(7t) = (5t)/(7t)
...cancel to get... t = 5/7
...and plug into calculator to get.... t = 0.714

But what if the equation is more complex? What if the equation is not easily reduced by hand? More complex equations, as long as they only have a single unknown variable, are easily analysed using the Solver function available on any Texas Instruments graphing calculator.

Specific instructions on how to use the Solver on your calculator are available in the instruction manual that came with your calculator. A "quick and dirty" guide to using the Solver on the TI-83 graphing calculator is outlined here, along with an example that follows the step-by-step procedure.

How to Use the Solver

1) Arrange the equation to be solved so that it equals zero.
Example: 0.7t2 = 48t -240 should be rearranged to get 0.7t2 -48t +240 = 0

2) Turn on the TI-83, hit the [Math] key, and choose "0) Solver" to get the Solver screen.

3) Enter your equation into the Solver.
Example: eqn: 0 = appears on the screen. You type in 0.7x2 - 48x +240 and hit [Enter]. Note that the "x-squared" key should be used instead of "2" in the equation.

4) Enter your guess for the answer.
Example:x= appears on the screen. Type in any guess -- it doesn't matter what. We'll use 0, so type a 0 in there.

5) Enter the bounds for the solution, if necessary.
bound={-1E99, 1E99} appears on the screen. This is the range of numbers that the calculator will use to look for a solution to your equation. You can ignore this range -- right now, it's set to search for any possible solution.

6) Start the Solver.
Use the button keys to move the cursor to the variable you want to solve for and press [Alpha] [Solve] (just above the [Enter] key.)
Example: Move the cursor to the line that says x=0 if it isn't already there and hit [Alpha] [Solve].

7) Wait for the Answer!
The calculator will display a small moving line in the upper right corner of the screen to indicate that it's working on the problem. After a few seconds the solution will appear next to the variable x.
Example:x=5.429.....

Voila! This is a solution to the equation. There MAY be other solutions, of course, and if you judge that this solution is meaningless in terms of the actual physics problem your trying to solve, you have to tweak the Solver a bit to find other solutions, as shown here:

8) To Find Additional Solutions to the Equation:
a) Change the bounds of the range where the calculator will look for a solution.
Example: Use buttons to choose {5.43, 1E99}, with the lower bound 5.08 just barely above our current solution.

b) Change the initial guess for x to any number in the bounds, say 5.43.

c) Hit [Alpha] [Solver] to have the Solver start searching for additional solutions. After a few seconds, x=63.1414.... appears on the screen, which is yet another solution to this equation.


If this solution seems closer to what you're expecting to see, use it. You may choose to look for additional solutions (although with a quadratic equation, we wouldn't expect any others). If we repeat step 8 again to try and get a new solution, the error message ERROR 27 NO SIGN CHANGE appears, which is the Solver's way of saying "Sorry, no more solutions!"

Using the Solver to help you find solutions to complex equations is just one of the ways that graphing calculators can assist your progress in physics. Please make sure, however, that you don't become TOO dependent on the calculator. Being able to manipulate variables and equations "by hand", as well as being able to substitute and solve equations in several unknowns is a valuable skill that cannot be replaced with a calculator, however powerful it may be.