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Question

Which constant must be added and subtracted to solve the quadratic equation $$9x^2 + \dfrac{3}{4}x - \sqrt{2} = 0$$ by the method of completing the square ?


A
18
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B
164
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C
14
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D
964
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Solution

The correct option is B $$\dfrac{1}{64}$$
Given equation is $$9x^2 + \dfrac{3}{4}x - \sqrt{2} = 0$$
$$\Rightarrow (3x)^2 + 2\left(\dfrac{1}{8}\right)(3x) - \sqrt{2} = 0$$

Hence, to make it a perfect square we must add and subtract $$\left(\dfrac{1}{8}\right)^2=\dfrac1{64}$$

Mathematics

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