Question

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

• A. $\frac{1}{8}$
• B. $\frac{1}{64}$
• C. $\frac{1}{4}$
• D. $\frac{9}{64}$

Answer 1

The correct option is B $\frac{1}{64}$

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

$\Rightarrow (3x{)}^2+2\left(\frac{1}{8}\right)(3x)-\sqrt{2}=0$

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