Factorization by Completing the Square


 
 
Concept Explanation
 

Factorization By Completing The Square Method

This method is based on the following fact, If

a^2 = b, ;where ;b geq 0, then ; a=pm sqrt b

Using this fact in solving a quadratic equation we will convert the left hand side into a perfect square. The concept can be better understood with the help of an illustration

Illustration: Find the roots of 2x^2-7x+3 =0

Step 1: Shift the constant term to Right Hand Side

                 2x^2-7x=-3

Step 2: Divide both side with the coefficient of  x^2 i.e. 2

                 x^2-frac{7}{2}x = -frac{3}{2}

Step 3: Add the square of half the coefficient of x to both side

x^2-2left ( frac{7}{4} right )x +left ( frac{7}{4} right )^2 = -frac{3}{2}+left ( frac{7}{4} right )^2

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Sample Questions
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Question : 1

What should be added to 2x^2-7x to make it a perfect square

Right Option : B
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Question : 2

What should be added to large large 4x^2 + 3x to make it a perfect square

Right Option : B
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Explanation
Question : 3

What should be added to large large frac{4}{9}x^2 + frac{16}{3}x+2 to make it a perfect square

Right Option : C
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Explanation
 
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