3 Simple Ways to Solve Quadratic Equations

The name Quadratic comes from the word “Quad”, meaning the “Square”, it is due to the fact the variable gets a square value in the quadratic equation, like  ax² + bx + c = 0.

Here the value of the variable “X” is a square value. The quadratic equation is widely used in Mathematics to solve various problems. The quadratic equation is also called an equation of the degree of “2” because the variable “X” has the power of 2, which is also called a square value. We can use the quadratic formula calculator to solve a quadratic equation, we can solve the quadratic equation by using different methods like factoring the quadratic education, completing the square, by putting the values in the quadratic formula, and by substitution method, and much more. 

We are using the quadratic equation in everyday life, as when we are calculating the areas, or when calculating the speed of an object. The quadratic equation is commonly used in statics and the business world to determine the various solutions to the problems. The quadratic formula calculator can be used by students to find the roots of quadratic equations. As you need the roots to put in other equations to solve the question.

The standard form of the quadratic equation

The simple form of the quadratic equation usually has one value of  “X” having a square value, the standard form of the quadratic equation is ax² + bx + c = 0. Where x is a variable, and its value is unknown and a, b and c are the coefficient of the equation. The values of the coefficient “a” can’t be equal to Zero. The students can use the quadratic formula calculator for solving the question of the derivation and integration as they quickly require the roots of the quadratic equation to solve the question.

Methods of solving the quadratic equation

There are three basic methods to solve a quadratic equation in mathematics:

  • The factorization method  
  • The completing square method
  • Using the quadratic formula

The other method to solve the quadratic equation is the graphical method to solve a quadratic equation. But students find it a little difficult to understand, as you have to draw the graphical values and put the values in the graph to get the solution of the quadratic equation. You can use the quadratic formula calculator for finding the solution of the quadratic equation. The graphical method is a little length process to solve the quadratic equation. It is better to increase general understanding of how quadratic equations are formulated. For simplification, you can use the quadratic equation solver to quickly find the solution of your equation.

Now we try to understand how we can find the solution of the quadratic equation by using the above mentioned three methods:

The factorization method:

The solution of the quadratic equation by using the factorization method is the fastest method to find the roots of the equation. The quadratic formula calculator helps you to find the factors of your quadratic equation.

Now consider an example to understand the solution of the quadratic equation by the factorization method.

                                        x 2 – 5x = – 10

In the next step the equation would become:

                                       x 2 – 5 x + 10 = 0

Now you have to follow the steps in sequence.

  • Look at the coefficient “a”, in this situation the value of the “a ” is “1”, Multiply it with the “c”. In this case, we will get the value “10”.
  • Now find two integers, when we add them, we get exactly “– 5” and when we multiply them we get “ +10”.
  • In this case, the integers are (– 2 and – 3) as when we add them we exactly get the value (– 5) and when we multiply them we get the values (+10)
  • So the factors of the above equations are (x– 2)(x– 3)

Solve these factors we will get the roots of the quadratic equations:

                    (x– 2)(x– 3)=0

               x– 2=0         and           x– 3=0      

                x=2                              x=3

Both the values of ( 2, 3) are the solutions of the above-mentioned quadratic equation. The quadratic equation calculator helps us to find the roots of the quadratic equation. As we need the roots quickly when solving lengthy problems. The roots of the quadratic equation can be found by using the quadratic formula calculator.

The completing square method:

The second basic method of solving the quadratic equation is the completing square method, to find both imaginary and real roots. As we can’t use the completing square method to find the imaginary roots of a quadratic equation.  We can use the quadratic formula solver to solve the quadratic equation when solving equation by the completing square method.

We will try to understand the completing square method:

  • Now first turn the equation into its standard form ax 2 + bx + c=0
  • Now f turn the equation into this form ax 2 + bx = – c
  • Make sure a=1((if a ≠ 1), you have to multiply the equation by “1/a” throughout the equation.
  • Use the value of b from this new form of the equation and add equationon both sides of the equation to form a perfect square on the left side of the equation.
  • Now find the square root on th both sides of the equation 
  • Solve the equation to find the solution and determine the roots whether it is imaginary or real. 

Students find it difficult to solve the imaginary and irrational roots, so you can use the quadratic formula, calculator to find such roots.

The quadratic formula:

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    We can also use the quadratic formula to find the roots of the quadratic equation. We have to use the quadratic formula as we can’t solve some of the quadratic equations by using the factorization method, so we have to use the quadratic formula to find the roots of the quadratic equation. We can use the quadratic calculator to find the roots of the quadratic equation. We use the quadratic formula for finding the imaginary and irrational roots, you can use the quadratic formula calculator to find such roots for your convenience.

    We have to solve quadratic equations, having imaginary, irrational roots, so we are forced to use the quadratic formula. In this case, we have to use the quadratic formula:

    equation

    We have to take the value of the a, b, and c from the quadratic equation ax 2 + bx + c = 0 to put the values in the quadratic formula, and to find the roots of the quadratic equation.

    The use of the quadratic equation is enormous in the field of mathematics, we can find the solution of the quadratic equation by using the three methods, the factorization method, the completing square method, and the using the quadratic formula. The quadratic formula calculator is a way to find the roots of the quadratic equation. You can check that you have solved the problem correctly, especially when you are solving the imaginary and irrational roots. The factorization method is the fastest method to find the roots of the quadratic equation, if the roots are real otherwise, we have to use the completing square method or the quadratic formula to find the roots of the quadratic equation.                                

    Hope this article will help you.

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    Sandipan Mukherjee
    I manage online marketing at Stoodnt, Inc. I did my MBA from PUNE INSTITUTE OF BUSINESS MANAGEMENT. I’m into Digital Marketing, Website Building, Blogging & Infographics creating. If you have any business related queries, drop a mail at [email protected]
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