How to Solve Quadratic Equations

Have you been wondering how to solve quadratic equations?

These equations do look intimidating and more difficult to solve. But... don't worry, I am going to show you several methods for solving quadratic equations.

You can solve a simple quadratic equation using the same rules that you used when solving linear equations. We'll discover that method in this lesson.

You can also solve quadratic equations by using the Quadratic Formula and by Factoring.

For right now, let's focus our attention on solving simple quadratic equations using a few strategies that you are already familiar with.

There is, of course, one new skill that you must apply. That is using square roots. Knowing how to take the square root of a number is essential to this lesson, so please review this lesson if needed.

Let's look at our first example, which is an extremely basic equation. Take note of the use of the square root.

Example 1

For Example 2, we will look at a two-step quadratic equation. In this example we will get rid of the constant first and then take the square root of x² in order to get x by itself. Take a look.

Example 2

Now we'll look at an example that it a little more complex because it requires one more step in order to get rid of the coefficient of x².

Example 3

And... for one more example - Just to make sure that you really understand this concept before moving on.

Our last example will demonstrate what happens when your last step does not result in a perfect square.

Example 4

Ok, are you ready to try a couple on your own? If you want to see an application of this skill in word problem format, be sure to check out the practice problems.

Practice Problems

Answer Key

Problem 1

Problem 2

Great Job! You are now prepared to learn how to solve quadratic equations using other methods.