How can you solve a quadratic equation?

For a Mathematics student, the most common problem related to Algebra is the solution of a quadratic equation. As a student, you must have seen problems where you have been asked to find the roots of this type of equation. 

Do you want to learn what this equation is? Are you looking to understand all methods that can be used to solve it? You should read this blog till the end because we have wrapped all methods in this guide. Let us show you the solution to this equation step by step! 

What is a quadratic equation? 

In Mathematics, the quadratic equation is a particular type of equation in which the maximum power of the variable is “2”. Simply, if the variable (x, y, and z) has a maximum power of “2” in an equation, it will be called a quadratic equation. The general form of a quadratic equation is given below, 

ᵃˣ² ⁺ ᵇˣ ⁺ ᶜ ⁼ ⁰

As you can see, the maximum power of “x” in this equation is “2”. The variable can be different in your related problem but the maximum power must be “2”. In the general form, “a”, “b”, and “c” represents the numbers that are used as coefficients and constants. 

Methods to solve a quadratic equation 

Generally, there are three methods that you can use to solve a quadratic equation. Doesn’t matter how complex an equation is, you can easily solve it using any of these methods. In the following sections, we have discussed them briefly to let you know how to go with a specific method. 

  1. Factorization 

It is the simplest way to solve a quadratic equation in which you have to split the central part of the equation into two parts. In simple words, you have to divide the coefficient of “x” into two sections to factorize the whole equation. 

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The factors that you will make of that coefficient should be equal to the original number if they are added or subtracted. Another condition that should be fulfilled is that the multiplication of those two factors will be equal to the product of the coefficient of ˣ²  and the constant number.

If you have found two factors of the central part of the equation that are fulfilling the above conditions, you are good to go with this method. Because of the multiplication process, this method is only suitable for smaller values of coefficients and constants. You may find it difficult when dealing with a larger number used as a constant in the concerned equation. 

  1. Completing Square 

Another method that can be used for solving a quadratic equation is through completing a square. It is not used widely because of the involvement of different steps that should be taken in a proper way. 

But this method can be effective in solving a quadratic equation as the main task is to complete the square on both sides of the equation. Once you have done this, you only have to take the square root of both sides and then solve linear equations that have been formed from this method. 

Here are some steps that you have to follow for solving a quadratic equation using this approach. 

  • Take the constant to the other side of the equation 
  • Make sure the constant is on one side while the other parts are on the other side
  • Divide the whole equation by the coefficient of ˣ²
  • Now, multiply the coefficient of “x” by “1/2” 
  • Add the square of the resultant of this multiplication on both sides
  • The left side will become the whole square of some terms 
  • Solve the right side of the equation to get one whole number 
  • Take the square root on both sides of the equation 
  • Now, you have converted the quadratic equation into two linear equations
  • Solve them to find the roots of the given equation 
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These are some general steps that you have to take to solve an equation using a completing square method. It may be hectic to solve an equation through it manually because of the multiple steps. You can use a maths online calculator to make the process simple and fast to complete your assignments. 

  1. Quadratic Formula 

Third and the easiest way to solve a quadratic equation is through Quadratic Formula. In this method, you only have to put the values in this formula and solve it through basic Mathematical operations. 

At the end of the process, you will get the values/roots of the variable that fulfills the equation to be true. Here is the general form of a quadratic equation:

How can you solve a quadratic equation?

You can easily understand the terms used in the above formula by comparing them with the above general form of the equation. By solving this equation, you will get two values for the variable that is “x” in the above formula. 

Final Words 

By reading this comprehensive guide, you must have got an idea about quadratic equations and the methods to solve them. We have discussed them briefly to make sure that everyone can understand them. 

Doesn’t matter whether you are a high school student or studying in the lower grades, you can understand these methods. You can also solve an equation using a maths online calculator if you want to get the task done without manual effort.

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