SOLVING QUADRATIC EQUATIONS BY FACTORING USING BOX METHOD 

Factoring Quadratic Expressions Using Box Method - Steps

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

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

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

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. 

16x² - 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

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

So, the solution is {1/10, 1/10}.

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