Solving Quadratic Equations using Factorising and Formula | Maths Tutorials from an Oxford Graduate

Learn how to solve quadratic equations using factorising or the quadratic formula with an Oxford Graduate. Many mathematical equations involve an x^2 term. These are called quadratic and solving them requires more than the ability to transpose or rearrange. There are three analytical methods available for solving quadratic equations: factorising, the quadratic formula or completing the square. This lesson covers how to solve by factorising or the quadratic formula. Completing the square is covered in a separate video (coming soon).

The video covers what we mean by a quadratic equation and how to decide on which method is best to use to solve them. We will also discuss why there are usually two solutions to a quadratic equation but why sometimes there may only be one or even no solutions and how you can check the equation to find out how many solutions there will be. Various different examples are discussed, each with their own difficulties. This means that you will be able to solve any quadratic equation you may meet!

Please note: Quadratic equations with no solutions can be solved using complex or imaginary numbers. This is not required for GCSE but you can find out how to do this in the lesson introducing complex numbers: (coming soon).

If you want to watch a specific part of the lesson, click on the following links to take you to the relevant part of the video:
What we mean by quadratic equation: 0:11
Why there are two possible solutions to a quadratic equation: 3:50
How to solve a quadratic equation by factorising: 7:03
Why some quadratic equations have only one solution: 11:51
Test yourself at solving by factorising: 15:03
How to solve a quadratic equation using the quadratic formula: 18:05
Why some quadratic equations have no real solutions: 30:40
How to test the number of solutions to a quadratic equation: 32:48
Test yourself at finding the number of solutions: 34:28
Test yourself at solving quadratic equations by factorising or using the formula: 38:11

The following examples are covered in this lesson:
x^2 – 5x – 6 = 0 : 6:59
x^2 + 1 = 2x : 10:38
x^2 – 4 = 0 : 13:17
x^2 – 4x = 7 : 18:02
1 – 4x = 3x^2 : 25:09
2x^2 + x = x^2 – 4 : 29:28

Previous knowledge required:

How to factorise quadratics:    • How to Factorise Quadratics | Maths T...  
How to solve equations: (coming soon)
How to transpose / rearrange algebraic equations: (coming soon)
How to do substitution: (coming soon)

Where to go next:

How to complete the square: (coming soon)
How to solve simultaneous equations involving quadratics: (coming soon)
How to solve quadratic equations with no real solutions: (coming soon)

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OxMath provides easy to understand maths tutorials for learners, teachers and parents. The lessons are given by an Oxford Graduate with a First class Masters degree in Engineering, a PGCE in Maths and experience as a maths teacher at various schools and FE facilities.

The lessons contain thorough explanations aimed at achieving a comprehensive understanding rather than rote learning. Although you will learn the methods required for school and passing exams, you will also gain knowledge of the underlying theory and how the methods work. This leads to a better understanding of maths in general, a greater ability to apply the maths when required and better grades.

The playlists are sorted by key stage and topic area but not by grade, as OxMath strongly believes that there are no limits to a learners potential and nobody should be put off by a topic's supposed grade. Instead, the videos are linked so you know what previous knowledge is required and where to go next!

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