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.
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
|
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}.
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