Solve (x-1/3)^2=7/9

$$( x - \frac { 1 } { 3 } ) ^ { 2 } = \frac { 7 } { 9 }$$

Solve for x

$$x = \frac{\sqrt{7} + 1}{3} \approx 1.215250437$$

$$x=\frac{1-\sqrt{7}}{3}\approx -0.54858377$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$x-\frac{1}{3}=\frac{\sqrt{7}}{3} x-\frac{1}{3}=-\frac{\sqrt{7}}{3}$$

Add \frac{1}{3} to both sides of the equation.

$$x-\frac{1}{3}-\left(-\frac{1}{3}\right)=\frac{\sqrt{7}}{3}-\left(-\frac{1}{3}\right) x-\frac{1}{3}-\left(-\frac{1}{3}\right)=-\frac{\sqrt{7}}{3}-\left(-\frac{1}{3}\right)$$

Subtracting -\frac{1}{3} from itself leaves 0.

$$x=\frac{\sqrt{7}}{3}-\left(-\frac{1}{3}\right) x=-\frac{\sqrt{7}}{3}-\left(-\frac{1}{3}\right)$$

Subtract -\frac{1}{3} from \frac{\sqrt{7}}{3}.

$$x=\frac{\sqrt{7}+1}{3}$$

Subtract -\frac{1}{3} from -\frac{\sqrt{7}}{3}.

$$x=\frac{1-\sqrt{7}}{3}$$

The equation is now solved.

$$x=\frac{\sqrt{7}+1}{3} x=\frac{1-\sqrt{7}}{3}$$