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# Choose the correct answer from the given four options in the following questions:

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

**A)** $ \frac{1}{8} $

**(B)** $ \frac{1}{64} $

**(C)** $ \frac{1}{4} $

**(D)** $ \frac{9}{64} $

To do:

We have to find the correct answer.

Solution:

$9 x^{2}+\frac{3}{4} x-\sqrt{2}=0$

$(3 x)^{2}+\frac{1}{4}(3 x)-\sqrt{2}=0$

Let $3 x=k$

This implies,

$k^{2}+\frac{1}{4}k-\sqrt{2}=0$

$k^{2}+\frac{1}{4}k+(\frac{1}{8})^{2}-(\frac{1}{8})^{2}-\sqrt{2}=0$

$(k+\frac{1}{8})^{2} =\frac{1}{64}+\sqrt{2}$

$(k+\frac{1}{8})^{2}=\frac{1+64\sqrt{2}}{64}$

Therefore,

$\frac{1}{64}$ must be added and subtracted to solve the given equation.

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