Solve {left(x-1/9right)}^2=4/81

$${ \left(x- \frac{ 1 }{ 9 } \right) }^{ 2 } = \frac{ 4 }{ 81 }$$

Solve for x

$$x=\frac{1}{3}\approx 0.333333333$$

$$x=-\frac{1}{9}\approx -0.111111111$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$x-\frac{1}{9}=\frac{2}{9} x-\frac{1}{9}=-\frac{2}{9}$$

Add \frac{1}{9} to both sides of the equation.

$$x-\frac{1}{9}-\left(-\frac{1}{9}\right)=\frac{2}{9}-\left(-\frac{1}{9}\right) x-\frac{1}{9}-\left(-\frac{1}{9}\right)=-\frac{2}{9}-\left(-\frac{1}{9}\right)$$

Subtracting -\frac{1}{9} from itself leaves 0.

$$x=\frac{2}{9}-\left(-\frac{1}{9}\right) x=-\frac{2}{9}-\left(-\frac{1}{9}\right)$$

Subtract -\frac{1}{9} from \frac{2}{9} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$x=\frac{1}{3}$$

Subtract -\frac{1}{9} from -\frac{2}{9} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$x=-\frac{1}{9}$$

The equation is now solved.

$$x=\frac{1}{3} x=-\frac{1}{9}$$