SOLVING QUADRATIC EQUATIONS BY FACTORING USING BOX METHOD 

Factoring Quadratic Expressions Using Box Method - Steps

Step 1 :

Draw a box, split it into four parts.

Write the first and last term in the first and last box respectively.

Step 2 :

We have to multiply the coefficient of x2 term and constant term.

Now, we have to decompose the value that we get in step 2, such that the product must be equal to the value in step 2 and simplified value must be equal to the middle term. 

Step 3 :

Write those values in the empty boxes. Factor horizontally and vertically

Step 4 :

Write the horizontal and vertical terms as pairs. By equating each factor to zero, we will get the values of x.

Solved Examples

Example 1 :

Solve the following quadratic equation : 

x2 - 3x - 10  =  0

Solution : 

From the box method, we find the factors.

The factors are (x + 2) and (x - 5). 

Then, 

(x + 2)(x - 5)  =  0

x + 2  =  0

x  =  -2

x - 5  =  0

x  =  5

So, the solutions is {-2, 5}.

Example 2 :

Solve the following quadratic equation : 

2x2 + x - 6  =  0

Solution : 

From the box method, we find the factors.

The factors are (2x - 3) and (x + 2).

Then, 

(2x - 3)(x + 2)  =  0

2x - 3  =  0

2x  =  3

x  =  3/2

x + 2  =  0

x  =  -2

So, the solution is {3/2, -2}.

Example 3 :

Solve the following quadratic equation : 

√2x2 + 7x + 5√2  =  0

Solution : 

From the box method, we find the factors.

The factors are (x + √2) and (√2x + 5). 

Then, 

(x + √2)(√2x + 5)  =  0

x + √2  =  0

x  =  -√2

√2x + 5  =  0

√2x  =  -5

x  =  -5/√2

So, the solution is {-√2, -5/√2}.

Example 4 :

Solve the following quadratic equation : 

2x2 - x + (1/8)  =  0

Solution : 

In the above quadratic equation, multiply each side by 8. 

16x- 8 x + 1  =  0

From the box method, we find the factors.

The factors are (4x - 1) and (4x - 1). 

Then, 

(4x - 1)(4x - 1)  =  0

4x - 1  =  0

4x  =  1

x  =  1/4

4x - 1  =  0

4x  =  1

x  =  1/4

So, the solutions {1/4, 1/4}.

Example 5 :

Solve the following quadratic equation : 

100x2 - 20 x + 1  =  0

Solution : 

From the box method, we find the factors.

The factors are (10x - 1) and (10x - 1).

Then, 

(10x - 1)(10x - 1)  =  0

10x - 1  =  0

10x  =  1

x  =  1/10

10x - 1  =  0

10x  =  1

x  =  1/10

So, the solution is {1/10, 1/10}.

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.

©All rights reserved. onlinemath4all.com

Recent Articles

  1. SAT Math Resources (Videos, Concepts, Worksheets and More)

    Dec 23, 24 03:47 AM

    SAT Math Resources (Videos, Concepts, Worksheets and More)

    Read More

  2. Digital SAT Math Problems and Solutions (Part - 91)

    Dec 23, 24 03:40 AM

    Digital SAT Math Problems and Solutions (Part - 91)

    Read More

  3. Digital SAT Math Problems and Solutions (Part - 90)

    Dec 21, 24 02:19 AM

    Digital SAT Math Problems and Solutions (Part - 90)

    Read More