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
B
164
C
14
D
964

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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