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

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.

## More by this Author

- 26
A compound shape is a shape that is made up from other simple shapes. In this article we will be working out the area of a L shape (made up from 2 rectangles). To find the area of a compound shape, follow these simple...

- 0
The density, mass and volume triangle is as follows: So if you wanted to work out the density, you would cover up density in the magic triangle to give: Density = Mass/Volume (since mass is above volume) So if...

- 0
The surface area of a triangular prism can be found in the same way as any other type of prism. All you need to do is calculate the total area of all of the faces. A triangular prism has 5 faces, 3 being rectangular and...

## Comments 2 comments

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.

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