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. $\frac{1}{8}$
• 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 $9x^2+\frac{3}{4}x-2=0$
$\Rightarrow (3x{)}^2+\frac{1}{4}(3x)-2=0$
On putting 3x = y, we have $y^2+\frac{1}{4}y-2=0$
$\Rightarrow y^2+\frac{1}{4}y+{\left(\frac{1}{8}\right)}^2-{\left(\frac{1}{8}\right)}^2-2=0\Rightarrow {(y+\frac{1}{8})}^2=\frac{1}{64}+2\Rightarrow {(y+\frac{1}{8})}^2=\frac{129}{64}$

$\Rightarrow y=\pm \frac{\sqrt{129}}{8}-\frac{1}{8}$

$\Rightarrow y=\frac{\sqrt{129}-1}{8}or\frac{-(\sqrt{129}+1)}{8}$

Thus, $(\frac{1}{8}{)}^2=\frac{1}{64}$ must be added and subtracted to solve the given equation.