Solve 3(x-1/3)^2-13/3=0

$$3 ( x - \frac { 1 } { 3 } ) ^ { 2 } - \frac { 13 } { 3 } = 0$$

Solve for x

$$x = \frac{\sqrt{13} + 1}{3} \approx 1.535183758$$

$$x=\frac{1-\sqrt{13}}{3}\approx -0.868517092$$

Steps by Finding Square Root

Add \frac{13}{3} to both sides of the equation.

$$3\left(x-\frac{1}{3}\right)^{2}-\frac{13}{3}+\frac{13}{3}=\frac{13}{3}$$

Subtracting \frac{13}{3} from itself leaves 0.

$$3\left(x-\frac{1}{3}\right)^{2}=\frac{13}{3}$$

Divide both sides by 3.

$$\frac{3\left(x-\frac{1}{3}\right)^{2}}{3}=\frac{\frac{13}{3}}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$\left(x-\frac{1}{3}\right)^{2}=\frac{\frac{13}{3}}{3}$$

Divide \frac{13}{3} by 3.

$$\left(x-\frac{1}{3}\right)^{2}=\frac{13}{9}$$

Take the square root of both sides of the equation.

$$x-\frac{1}{3}=\frac{\sqrt{13}}{3} x-\frac{1}{3}=-\frac{\sqrt{13}}{3}$$

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

$$x-\frac{1}{3}-\left(-\frac{1}{3}\right)=\frac{\sqrt{13}}{3}-\left(-\frac{1}{3}\right) x-\frac{1}{3}-\left(-\frac{1}{3}\right)=-\frac{\sqrt{13}}{3}-\left(-\frac{1}{3}\right)$$

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

$$x=\frac{\sqrt{13}}{3}-\left(-\frac{1}{3}\right) x=-\frac{\sqrt{13}}{3}-\left(-\frac{1}{3}\right)$$

Subtract -\frac{1}{3} from \frac{\sqrt{13}}{3}.

$$x=\frac{\sqrt{13}+1}{3}$$

Subtract -\frac{1}{3} from -\frac{\sqrt{13}}{3}.

$$x=\frac{1-\sqrt{13}}{3}$$

The equation is now solved.

$$x=\frac{\sqrt{13}+1}{3} x=\frac{1-\sqrt{13}}{3}$$