Which constant can be added and subtracted from the equation $9{\mathrm{x}}^2-2\sqrt{2}\mathrm{x}+8=0$ to solve it by the method of completing the square?

 

Given equation: $9{\mathrm{x}}^2-2\sqrt{2}\mathrm{x}+8=0$

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

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

Thus, ${\left(\frac{\sqrt{2}}{3}\right)}^2=\frac{2}{9}$ can be added and subtracted from the given equation.