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Solving quadratic equations easily using the quadratic formula (with a calculator)

Updated on July 7, 2010

If you are asked to solve a quadratic equation then you need to use the quadratic formula.

x = [-b ± √{b² - 4ac}]/2a

Quadratic equations which look like ax² + bx + c = 0 can be solved using the quadratic formula shown above. In these worked questions shown below, you will be rounding off your answer either to 1 decimal place or to 2 decimal places.

Quadratic Formula Question 1

Use the quadratic formula to solve the quadratic equation:

3x² -2x -7 = 0

Round your solutions to 1 decimal place.

To begin with write down the values of a, b and c.

a = (3), b = (-2) and c = (-7).

Notice that all the numbers have had a bracket put around them. This will eliminate any errors when you type them in on your calculator. Also make sure you have a new scientific calculator that allows you to enter fractions.

Next, substitute these numbers into the quadratic formula:

x = [-b ± √{b² - 4ac}]/2a

x = [-(-2) ± √{(-2)² - 4(3)(-7)}]/2(3)

Now type this exactly into your calculator to get the first solution (change ± to + first of all)

x = [-(-2) + √{(-2)² - 4(3)(-7)}]/2(3)

x = 1.9 to 1 decimal place.

Then get the next solution by changing the ± sign to a -.

x = [-(-2) - √{(-2)² - 4(3)(-7)}]/2(3)

x= -1.2 to 1 decimal place.

So your two solution are x = 1.9 and x = -1.2. These are the places where the quadratic crosses the x axis and are called the roots.

Quadratic Formula Question 1

Use the quadratic formula to solve the quadratic equation:

2x² -x -9 = 0

Round your solutions to 2 decimal places.

To begin with write down the values of a, b and c.

a = (2), b = (-1) and c = (-9).

Notice that the number before x is -1.

Next, substitute these numbers into the quadratic formula:

x = [-b ± √{b² - 4ac}]/2a

x = [-(-1) ± √{(-1)² - 4(2)(-9)}]/2(2)

Now type this exactly into your calculator to get the first solution (change ± to + first of all)

x = [-(-1) + √{(-1)² - 4(2)(-9)}]/2(2)

x = 2.39 to 2 decimal places.

Then get the next solution by changing the ± sign to a - sign.

x = [-(-1) + √{(-1)² - 4(2)(-9)}]/2(2)

x= -1.89 to 2 decimal places.

So your two solutions are x = 2.39 and x = -1.89. These are the places where the quadratic equation crosses the x axis and are called the roots.

For some more tips on using the quadratic formula then click here.

For examples on using the quadratic formula leaving your answers in surd form then click here.

Comments

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  • profile image

    Fletcher Tomalty 

    7 years ago

    There's a free online quadratic formula calculator http://quadratic-formula-calculator.com/ that does all this automatically, you don't even need to use a calculator for it.

  • AEvans profile image

    Julianna 

    8 years ago from SomeWhere Out There

    I enjoyed this lesson on how to solve quadratic equations by using a calculator it is always nice to learn something new! Thumbs up ! :)

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