Question

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

• A. $\frac{1}{64}$
• B. $\frac{1}{576}$
• C. $\frac{1}{144}$
• D. $\frac{127}{64}$

Answer 1

Answer: (B)

$\frac{1}{576}$

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

Dividing by $9$ on both sides we get,

$x^2+\frac{x}{12}+\frac{2}{9}=0$

$x^2+\frac{x}{12}=-\frac{2}{9}$

Third term $={(\frac{1}{2}\times \text{coefficient of}x)}^2$

$={(\frac{1}{2}\times \frac{1}{12})}^2$ = ${\left(\frac{1}{24}\right)}^2=\frac{1}{576}$

Adding $\frac{1}{576}$ on both sides we get,

$\therefore x^2+\frac{x}{12}+\frac{1}{576}$ = $\frac{1}{576}-\frac{2}{9}$

${(x+\frac{1}{24})}^2=$ $\frac{1}{576}-\frac{2}{9}$

Hence, option $B$.