Solve 1/3(x-4)^2-3=0

$$\frac { 1 } { 3 } ( x - 4 ) ^ { 2 } - 3 = 0$$

Solve for x

$$x=7$$

$$x=1$$

Steps by Finding Square Root

Add 3 to both sides of the equation.

$$\frac{1}{3}\left(x-4\right)^{2}-3+3=3$$

Subtracting 3 from itself leaves 0.

$$\frac{1}{3}\left(x-4\right)^{2}=3$$

Multiply both sides by 3.

$$\frac{\frac{1}{3}\left(x-4\right)^{2}}{\frac{1}{3}}=\frac{3}{\frac{1}{3}}$$

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

$$\left(x-4\right)^{2}=\frac{3}{\frac{1}{3}}$$

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

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

Take the square root of both sides of the equation.

$$x-4=3 x-4=-3$$

Add 4 to both sides of the equation.

$$x-4-\left(-4\right)=3-\left(-4\right) x-4-\left(-4\right)=-3-\left(-4\right)$$

Subtracting -4 from itself leaves 0.

$$x=3-\left(-4\right) x=-3-\left(-4\right)$$

Subtract -4 from 3.

$$x=7$$

Subtract -4 from -3.

$$x=1$$

The equation is now solved.

$$x=7 x=1$$