Question

Question 7
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

Given equation is $9x^2+\frac{3}{4}x-\sqrt{2}=0$
$(3x{)}^2+\frac{1}{4}(3x)-\sqrt{2}=0$
On putting 3x = y, we have $y^2+\frac{1}{4}\left(y\right)-\sqrt{2}=0$
$y^2+\frac{1}{4}y+{\left(\frac{1}{8}\right)}^2-{\left(\frac{1}{8}\right)}^2-\sqrt{2}=0$
${(y+\frac{1}{8})}^2=\frac{1}{64}+\sqrt{2}$
${(y+\frac{1}{8})}^2=\frac{1+64+\sqrt{2}}{64}$
Thus, $\frac{1}{64}$ must be added and subtracted to solve the given equation by the method of completing the square.