Solving equations is a common task in algebra and other branches of mathematics. It involves finding the values of the unknown variables that make the equation true.
The TI-84 calculator has a built-in program that can solve equations for you, as long as you have one variable and the equation is in one of the following forms:
- Linear: ax + b = c
- Quadratic: ax2 + bx + c = 0
- Cubic: ax3 + bx2 + cx + d = 0
- Quartic: ax4 + bx3 + cx2 + dx + e = 0
In this article, we will show you how to use the equation solver on a TI-84 calculator, and provide some examples and tips along the way.
How to Access the Equation Solver
The equation solver can be accessed on a TI-84 calculator by following these steps:
- Press the MATH key and then press the right-arrow key to move to the NUM menu.
- Scroll down to option B:solve( and press ENTER. This will bring up the equation solver on the screen.
How to Use the Equation Solver
The equation solver has the following syntax:
solve(equation, variable, [guess])
where:
- equation: the equation you want to solve, using the appropriate symbols and parentheses
- variable: the variable you want to solve for, using the letter X
- guess: (optional) an initial estimate of the solution, which can speed up the process
If you omit the guess argument, the calculator will use zero as the default guess.
The equation solver will return the solution of the equation, or an error message if the equation cannot be solved.
Examples of Using the Equation Solver
Let’s look at some examples of how to use the equation solver on a TI-84 calculator.
Example 1: Linear Equation
Question: Solve the equation 3x – 5 = 10 for x.
Answer: To solve the equation, we need to use the equation solver with the following arguments:
solve(3x-5=10,X)
Press ENTER to get the answer:
X=5
This means that the solution of the equation is x = 5.
Example 2: Quadratic Equation
Question: Solve the equation x2 – 5x + 6 = 0 for x.
Answer: To solve the equation, we need to use the equation solver with the following arguments:
solve(X2-5X+6=0,X)
Press ENTER to get the answer:
X=2 or X=3
This means that the equation has two solutions: x = 2 or x = 3.
Example 3: Cubic Equation
Question: Solve the equation x3 – 6x2 + 11x – 6 = 0 for x.
Answer: To solve the equation, we need to use the equation solver with the following arguments:
solve(X3-6X2+11X-6=0,X)
Press ENTER to get the answer:
X=1 or X=2 or X=3
This means that the equation has three solutions: x = 1, x = 2, or x = 3.
Example 4: Quartic Equation
Question: Solve the equation x4 – 10x3 + 35x2 – 50x + 24 = 0 for x.
Answer: To solve the equation, we need to use the equation solver with the following arguments:
solve(X4-10X3+35X2-50X+24=0,X)
Press ENTER to get the answer:
X=1 or X=2 or X=3 or X=4
This means that the equation has four solutions: x = 1, x = 2, x = 3, or x = 4.
Tips and Tricks for Using the Equation Solver
Here are some tips and tricks for using the equation solver on a TI-84 calculator:
- To enter the equation, you can use the following symbols and keys on the calculator:
- X: the variable key, located above the STO> key
- =: the equals sign, located next to the decimal point
- +: the plus sign, located next to the ENTER key
- -: the minus sign, located next to the plus sign
- x: the multiplication sign, located above the plus sign
- /: the division sign, located above the minus sign
- ^: the exponent sign, located above the division sign
- (: the left parenthesis, located above the 8 key
- ): the right parenthesis, located above the 9 key
- To enter the guess, you can use any number that is close to the solution, or use the ANS key to use the previous answer as the guess.
- To see the other solutions of the equation, you can press the down arrow key to scroll through the list of solutions, or press the up arrow key to go back to the previous solution.
- To check your answer, you can substitute the solution into the equation and see if it makes the equation true. You can do this by pressing the 2nd key and then the ENTER key to recall the equation, and then replacing the X with the solution using the STO> key. For example, to check the solution x = 5 for the equation 3x – 5 = 10, you can press:
2nd ENTER 5 STO> X ENTER
The calculator will display:
3(5)-5=10
true
This means that the solution is correct.