How to Solve Equations on a Calculator

How to Solve Equations on a Calculator
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  • 0:01 A Scientific Calculator
  • 1:38 An Equation by Hand
  • 2:22 Using the Scientific…
  • 5:08 Example
  • 6:27 Other Scientific…
  • 8:17 Lesson Summary
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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

After watching this video lesson, you will know how to use a basic scientific calculator to help you solve your mathematical equations. You will learn how a scientific calculator makes it easier to calculate your mathematical expressions.

A Scientific Calculator

When you take standardized tests, you are sometimes allowed the use of a basic scientific calculator. For example, when you take the SATs, you are allowed - and in fact, are encouraged - to bring a calculator that you are familiar with. According to the SAT guidelines, all scientific calculators are allowable. A scientific calculator is a calculator that will calculate science, engineering, and mathematics problems.

You will see buttons for the three trig functions of sine [SIN], cosine [COS], and tangent [TAN]. You will also see buttons for common mathematical constants and functions such as pi [pi] (the mathematical constant pi), ln [ln] (natural log), and factorial [n!]. Knowing how to use this type of calculator will help you tremendously in your test taking.

There are many brands of scientific calculators out there. Each brand operates a little differently. You will need to become familiar with the way your scientific calculator works. For example, when performing trigonometric calculations, some calculators need you to enter the degrees first before choosing the appropriate trig function. Other calculators need you to enter the trig function followed by the degrees. So, for the trig function sin (60), you could be entering either [6] [0] [sin] or [sin] [6] [0]. Also, if you are working with angles, make sure your scientific calculator is using the appropriate angle measurement - either degrees or radians. You will see a button for [DEG] or [RAD]. In some calculators, one or the other will be the secondary function of a button.

An Equation By Hand

Let's take a look at how you can use this scientific calculator to solve an equation. Say, for example, you are asked to solve this equation:

Solve for x: 4.32 = 3x - 10 x pi

To do this without a calculator, you would follow the rules of solving for an unknown variable. You would take it one step at a time to isolate the variable. You would first add the ten pi to both sides; then you divide by 3 to isolate the variable. So, your isolated variable becomes:

x = (4.32 + 10 x pi) / 3

To find your answer, you evaluate all your numbers. Doing this by hand, as you can see, is not all that short or pretty.

Using the Scientific Calculator

Using a scientific calculator can help you solve these equations that much quicker and easier. Your scientific calculator can calculate decimals with ease, and you can use the pi number without approximating it with 3.14. Your scientific calculator should have a button just for pi. If not the button itself, then it will be a secondary function of one of the buttons.

Just because you're using a scientific calculator does not mean that you won't have to do any work. You still need to know your math because you still need to isolate your variable by hand. You need to do this part by hand as it tells you in what order to input your numbers and which operations to use to find your answer. Looking at what you've done so far, you see that you need to multiply the 10 by pi first. Then you need to add this number to 4.32. Then you divide what you get by 3 to find your answer.

Unlike your basic calculator, your scientific calculator will actually follow the order of operations. This means that if you enter 4.32 + 10 x pi, your scientific calculator will perform the multiplication first and then the addition. This helps you out as you can enter a mathematical expression that includes several numbers and several operations. Scientific calculators also have parentheses that you can use to force an operation before another. You use the parentheses the same way you use them in math problems. Remember, your parentheses tell you and your calculator to perform the operations inside first before performing any other calculations.

You can actually type in your problem as a string into your scientific calculator. You use the parentheses around the 4.32 + 10 x pi and then you divide by 3.

To enter this, you push the button for the left parentheses [(], then [4] [.] [3] [2] [+] [1] [0] [x] [pi] [)] [/] and then [3]. To get your answer, you push [=].

If you didn't have the parentheses, your calculator would perform the 10 x pi first, and then divide the 10 x pi by 3 before adding the resulting value to 4.32. With the parentheses, the calculator performs the math in the right order by multiplying the 10 by pi, adding it to the 4.32, and then dividing the resulting value by 3. It makes a big difference! Make sure you're using your parentheses when needed.

Your calculator spits out 11.91 as your answer. This is your answer. That was pretty easy. As you use your scientific calculator to help you solve problems, you are always making sure that you are entering the numbers and operations in the order needed for your particular scientific calculator.


Let's try another problem.

Solve: 11 = x^2 - 21.2

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