TI-84 Plus and TI-84 Plus Silver Edition Guidebook

Note:

To speed the drawing of integration graphs (when

fnInt(

is used in a Y= equation), increase the value of the

Xres

window variable before you press s.

Using the Equation Solver

Solver

Solver

displays the equation solver, in which you can solve for any variable in an equation. The equation is assumed to be equal to zero.

Solver

is valid only for real numbers.

When you select

Solver

, one of two screens is displayed.

• The equation editor (see step 1 picture below) is displayed when the equation variable

eqn

is empty.

• The interactive solver editor is displayed when an equation is stored in

eqn

.

Entering an Expression in the Equation Solver

To enter an expression in the equation solver, assuming that the variable

eqn

is empty, follow these steps.

1.

Select

B:Solver

from the

MATH

menu to display the equation editor.

2.

Enter the expression in any of three ways.

• Enter the expression directly into the equation solver.

• Paste a Y= variable name from the

YVARS

shortcut menu ( t a

) to the equation solver.

• Press y K, paste a Y= variable name from the

YVARS

shortcut menu, and press

Í. The expression is pasted to the equation solver.

The expression is stored to the variable

eqn

as you enter it.

3.

Press

Í or †. The interactive solver editor is displayed.

• The equation stored in

eqn

is set equal to zero and displayed on the top line.

• Variables in the equation are listed in the order in which they appear in the equation. Any values stored to the listed variables also are displayed.

Chapter 2: Math, Angle, and Test Operations 41

• The default lower and upper bounds appear in the last line of the editor

(

bound={

L

1

â

99,1

â

99}

).

• A

$ is displayed in the first column of the bottom line if the editor continues beyond the screen.

Note:

To use the solver to solve an equation such as

K=.5MV

2

, enter

eqn:0=K

N

.5MV

2

in the equation editor.

Entering and Editing Variable Values

When you enter or edit a value for a variable in the interactive solver editor, the new value is stored in memory to that variable.

You can enter an expression for a variable value. It is evaluated when you move to the next variable. Expressions must resolve to real numbers at each step during the iteration.

You can store equations to any

VARS Y-VARS

variables, such as Y1 or r6, and then reference the variables in the equation. The interactive solver editor displays all variables of all Y= functions recalled in the equation.

Solving for a Variable in the Equation Solver

To solve for a variable using the equation solver after an equation has been stored to

eqn

, follow these steps.

1.

Select

B:Solver

from the

MATH

menu to display the interactive solver editor, if not already displayed.

2.

Enter or edit the value of each known variable. All variables, except the unknown variable, must contain a value. To move the cursor to the next variable, press

Í or †.

Chapter 2: Math, Angle, and Test Operations 42

3.

Enter an initial guess for the variable for which you are solving. This is optional, but it may help find the solution more quickly. Also, for equations with multiple roots, the TI-84 Plus will attempt to display the solution that is closest to your guess.

The default guess is calculated as



.

2

4.

Edit

bound={lower,upper}

.

lower

and

upper

are the bounds between which the TI-84 Plus searches for a solution. This is optional, but it may help find the solution more quickly. The default is

bound={

L

1

â

99,1

â

99}

.

5.

Move the cursor to the variable for which you want to solve and press

ƒ \.

• The solution is displayed next to the variable for which you solved. A solid square in the first column marks the variable for which you solved and indicates that the equation is balanced. An ellipsis shows that the value continues beyond the screen.

Note:

When a number continues beyond the screen, be sure to press

~ to scroll to the end of the number to see whether it ends with a negative or positive exponent. A very small number may appear to be a large number until you scroll right to see the exponent.

• The values of the variables are updated in memory.

•

left

N

rt=diff

is displayed in the last line of the editor.

diff

is the difference between the left and right sides of the equation when evaluated at the calculated solution. A solid square in the first column next to

left

N

rt

indicates that the equation has been evaluated at the new value of the variable for which you solved.

Editing an Equation Stored to eqn

To edit or replace an equation stored to

eqn

when the interactive equation solver is displayed, press

} until the equation editor is displayed. Then edit the equation.

Equations with Multiple Roots

Some equations have more than one solution. You can enter a new initial guess or new bounds to look for additional solutions.

Further Solutions

After you solve for a variable, you can continue to explore solutions from the interactive solver editor. Edit the values of one or more variables. When you edit any variable value, the solid

Chapter 2: Math, Angle, and Test Operations 43