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Question

What number should be added to x2+6x to make it a perfect square?


A

36

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B

18

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C

9

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D

72

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Solution

The correct option is C

9


The identity (a+b)2=(a2+2ab+b2) represents a perfect square.
If we observe carefully we can see that x2+6x can be written in the form (a2+2ab+b2) by adding a constant.
x2+2(x)(3)+constant.
To make x2+6x a perfect square, divide the coefficient of x by 2 and add the square of the result to make this a perfect square.
Hence 62=3 and 32=9.
We should add 9 to make x2+6x a perfect square.


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