Methods of solving quadratic equations

Solving quadratic equations is quite an important skill in mathematics. Many situations in life can be modeled with quadratic equations. Before reading this lesson, you may want to study or review the lesson that shows what factoring is.

The goal of this lesson is to familiarize you with the numbers of ways or methods that are used to solve quadratic equations. Usually this involves factoring the equation first.

Three methods of solving quadratic equations

Below, we show the three different ways or methods to solve a quadratic equation.

• Solve by factoring: most popular

• Solve by completing the square: most complicated

• Solve using the quadratic formula: most straightforward.

Method #1: solving quadratic equations by factoring

This is the most popular way to solve quadratic equations. This method shows you how to solve quadratic equations of the form ax² + bx + c = 0, when a = 1 or when a is not equal to 1. When a = 1, it is quite straightforward! When a is equal to 1, it is somewhat tedious. You will need to do trial and error. Check the lesson to see how!

Most teachers, if not all of them, will show you how to factor quadratic equations using this method first.

Method #2: solve by completing the square

This is the most complicated way to solve quadratic equations.

This method shows you how to complete the square to solve quadratic equations. Pay close attention to all steps and learn it well!

The very Proof of the quadratic formula is entirely based on this technique.

Make sure you understand it, or you may struggle a lot to understand the proof of the quadratic formula.

Teachers will not usually show you how to factor quadratic equations by completing the square until you have mastered how to solve them by factoring.

Method #3: solve using the quadratic formula

This is the most straightforward way to solve any quadratic equations since all you need to do is to plug in numbers into the formula.

Method #1 has some limitations when solving quadratic equations. When answers are not integers, but real numbers, it is very hard or nearly impossible to find the solutions.

With this formula, you can solve any quadratic equations and it does not matter how complex the equation is or how weird the answer will be.