Solve (x-1/3)^2=20/9

$$( x - \frac { 1 } { 3 } ) ^ { 2 } = \frac { 20 } { 9 }$$

Solve for x

$$x = \frac{2 \sqrt{5} + 1}{3} \approx 1.824045318$$

$$x=\frac{1-2\sqrt{5}}{3}\approx -1.157378652$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$x-\frac{1}{3}=\frac{2\sqrt{5}}{3} x-\frac{1}{3}=-\frac{2\sqrt{5}}{3}$$

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

$$x-\frac{1}{3}-\left(-\frac{1}{3}\right)=\frac{2\sqrt{5}}{3}-\left(-\frac{1}{3}\right) x-\frac{1}{3}-\left(-\frac{1}{3}\right)=-\frac{2\sqrt{5}}{3}-\left(-\frac{1}{3}\right)$$

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

$$x=\frac{2\sqrt{5}}{3}-\left(-\frac{1}{3}\right) x=-\frac{2\sqrt{5}}{3}-\left(-\frac{1}{3}\right)$$

Subtract -\frac{1}{3} from \frac{2\sqrt{5}}{3}.

$$x=\frac{2\sqrt{5}+1}{3}$$

Subtract -\frac{1}{3} from -\frac{2\sqrt{5}}{3}.

$$x=\frac{1-2\sqrt{5}}{3}$$

The equation is now solved.

$$x=\frac{2\sqrt{5}+1}{3} x=\frac{1-2\sqrt{5}}{3}$$