How to Factor the Quadratic Equation to know Variable Quantity?

An algebraic equation is one of the common math problems which include linear, quadratic and other higher degree equations. Solving out these equations is difficult sometimes due to the tough coefficient. If your kid is facing any difficulties in solving the algebra homework, then you can help by knowing the easy method for its solution. You can access the digital platform in which you just have to enter the coefficient then you can achieve the variables.

Without the graphing calculator or algebraic calculator, it is difficult to solve but it is not so. You can use the formula method or use the factors to determine the variable values. How to factor is the most common question that would come to the mind of the learner.  

Quadratic Equation

How to solve the quadratic equations?

Before solving the quadratic equation, you should understand its basics. To understand the quadratic equation, consider an example as- 2x² + 6x + 9 = 0 

A quadratic equation is written above in which x is the variable, and the number with X is coefficients and remaining one is constant. To get the math help by the calculator, you just have to fill the coefficient and constant values into the software. You can easily get the variable value which may be negative or positive. On the other hand, you can use other methods. These methods are as-

Solve by formula method 

A and B are the coefficients of   and x respectively, and C is the constant value available in the algebraic expression. Here in the equation, you have  

A= 2

B = 6

And c = 9

Now put the value into the equation, you will get,

After solving the numerical expressions, you can get two values. One is negative, and other one is positive.

By Factor method

Factor method is nothing but breaking out the expression into two parts i.e. taking out the common factor from the expression. Also, it is the simple and fast method to get the variable values. In this method, you don’t need to remember the complex formula. To better understand the factor method, you should know how to factor the expression. Consider an example to understand the factor method better and solve the quadratic algebraic equation.

2x² + 6x + 9 = 0

Follow the steps-

2x² + 2x + 3x + 9 = 0

In this step, the central part is divided into two parts

Now, you have to select the common factor out, i.e.

2x² + 2x + 3x + 3 = 0

2x(x + 3) + 3(x + 3) = 0

Take out the common factor again,

2x(x + 3) + 3(x + 3) = 0

(x + 3) (2x + 3) = 0

Now, you have two factors i.e. (x + 3) and (2x + 3)

Keep both the factors equal to zero to achieve individual values

X+3 = 0

X = -3

Again,

2X + 3 = 0

2X = -3

X = -3/2

We have two values of X which are determined by the factor method i.e. X = -3, -3/2

By this method, we do not have to face any complex calculations as faced in formula method. Here the most complex calculation is to choose the common factor. Also, you can find the simple method, but these methods are best to get the accurate answers. To check the answer, you can put the variable value into the expression. If the quadratic equations become zero, then you have right variable values.