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: Simple Quadratic Equations


How to solve simple quadratic equations

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: Quadratic Equations


Simple quadratic equations


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: Lead Coefficient Greater Than One


Simple quadratic equations with a lead coefficient greater than one



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:  Simple Quadratic Equations




Great Job! You are now ready to learn about the Pythagorean Theorem.


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