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?

Question

KollegeApply · Accepted Answer

bb($\frac{1}{64}$) Explanation: 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 + $\frac{1}{4}$y - sqrt(2) = 0 `y^2 + $\frac{1}{4}$y + ($\frac{1}{8}$)^2 - ($\frac{1}{8}$)^2 - sqrt(2) = 0 (y + $\frac{1}{8}$)^2 = $\frac{1}{64}$ + sqrt(2) (y + $\frac{1}{8}$)^2 = (1 + 64 sqrt(2))/64 Thus, $\frac{1}{64}$` must be added and subtracted to solve the given equation.

AChoose Your Answer