When it comes to stepping up your math game from linear equations to the more complex ones – most people get scared. One of the best examples of an equation that can frighten beginners is the quadratic equation. Even though the equation itself is pretty innocent but the combination of those alphabets can definitely give you a scare if you don’t know what to do.
What is Quadratic Equation?
Simply put a quadratic equation is an equation that looks like this “ax² + bx + c = 0”. As you can guess ‘x’ is the variable that need to be solved. A, b, and c are numbers where ‘a’ is not 0. What makes this equation quadratic is the squared term which is (ax2).
Why Quadratic Equation is Important?
In daily life quadratic equation can be used to calculate the area of a room. You can measure the room to lay a new carpet or to install new furniture that will actually fit in your room. Quadratic equation is also commonly used to figure out the profit and being used in almost all of the business nowadays. It can also help you with the profit you need to make to overcome tax loss. Quadratic equation is also being used in the field of sports especially athletics. For the games based on throwing objects such as shot put, it can help you estimate the time it will reach to a specific target at a certain distance. Manipulating the force of throw can give you the results you want!
The use of quadratic equation in the practical arena cannot be denied. It is often considered to be one of the most sophisticated mathematical equation. It can calculate the values for you if you are trying to grow more crops or planning to fly a plane. This diverse implementation of the quadratic equation leads to a question – how to solve the equation.
Solving Quadratic Equation
There are more than one methods to solve a quadratic equation and it totally depends on you how you want to solve it. These methods are going to provide you with an introduction to four methods so you can pick the method which is easiest for you. Today, we are going to provide you with not one but four simple methods you can use to solve a quadratic equation which are stated below.
- Square Root Method
- Completing the Square
- Quadratic Formula
Let’s discuss each of these methods in detail so you can know which one is easier for you. By the end of this article – you are going to find your favorite method to solve quadratic equations.
Square Root Method
The Square Root method is used to solve any quadratic equation when ‘bx’ is 0. Move the constant to the right side of the equation and then divide both sides by ‘a’, now you will take the square root of the both side that will give you two values of ‘x’ – one will be positive and the other one will be negative.
Square Root Method Example:
4x² – 9 = 0
4x² = 9
x² = 9 / 4
x² = 3 / 2 or – (3 / 2)
(take square root of both sides, and remember, every square root has a negative counterpart)
2. Completing the Square
Another pretty simple method to solve quadratic equations is completing the square. You can create a perfect square on the left side of the equation by adjusting your constant (c). After squaring, this perfect squared can now be factored into two binomials which will be identical. You can now use these identical binomials to obtain the value for ‘x’.
Completing the square:
x² – 4x + 9 = 0 (original equation)
x² – 4x = -9 (subtract 9 from both sides)
x² – 4x + 4 = 5 (take half of b, then square it and add that value to both sides of the equation)
(x – 2)² = 5 (break your perfect square into its binomials, made up of x, the sign in front of b and the square root of your new c)
x – 2 = √5 or – √ 5 (take the square root of both sides)
x = 2 + √5 or 2 – √ 5 (add 2 to both sides)
The second approach to solve a quadratic equation is factoring. The concept behind factoring is to find the number pairs that can be multiplies together to produce ‘c’ and then summed to produce ‘b’. If you are able to find the right combination, you will get two binomials. These binomials can now be solved individually to get the value of ‘x’.
3. Quadratic Formula
The quadratic formula is one of the most widely used approach when it comes to solving quadratic equation. The formula looks like this
You put the values and get the answer which will be the value of ‘x’. There are various online calculators available to solve quadratic equation and trust us – they are going to live your life much easier.
With the help of these methods, you can now finally stop hating the quadratic equation. Understand the logic behind the equation and then select the method you want to invest in. It will take practice but after patient and time, you will be able to solve it correctly every single time!