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

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

Solve for x

$$x=\sqrt{10}+2\approx 5.16227766$$

$$x=2-\sqrt{10}\approx -1.16227766$$

Steps by Finding Square Root

Add \frac{7}{3} to both sides of the equation.

$$\frac{1}{3}\left(x-2\right)^{2}-\frac{7}{3}+\frac{7}{3}=1+\frac{7}{3}$$

Subtracting \frac{7}{3} from itself leaves 0.

$$\frac{1}{3}\left(x-2\right)^{2}=1+\frac{7}{3}$$

Add 1 to \frac{7}{3}.

$$\frac{1}{3}\left(x-2\right)^{2}=\frac{10}{3}$$

Multiply both sides by 3.

$$\frac{\frac{1}{3}\left(x-2\right)^{2}}{\frac{1}{3}}=\frac{\frac{10}{3}}{\frac{1}{3}}$$

Dividing by \frac{1}{3} undoes the multiplication by \frac{1}{3}.

$$\left(x-2\right)^{2}=\frac{\frac{10}{3}}{\frac{1}{3}}$$

Divide \frac{10}{3} by \frac{1}{3} by multiplying \frac{10}{3} by the reciprocal of \frac{1}{3}.

$$\left(x-2\right)^{2}=10$$

Take the square root of both sides of the equation.

$$x-2=\sqrt{10} x-2=-\sqrt{10}$$

Add 2 to both sides of the equation.

$$x-2-\left(-2\right)=\sqrt{10}-\left(-2\right) x-2-\left(-2\right)=-\sqrt{10}-\left(-2\right)$$

Subtracting -2 from itself leaves 0.

$$x=\sqrt{10}-\left(-2\right) x=-\sqrt{10}-\left(-2\right)$$

Subtract -2 from \sqrt{10}.

$$x=\sqrt{10}+2$$

Subtract -2 from -\sqrt{10}.

$$x=2-\sqrt{10}$$

The equation is now solved.

$$x=\sqrt{10}+2 x=2-\sqrt{10}$$