Solve 3left(x-2right)^2-64=0

$$3 { \left(x-2 \right) }^{ 2 } -64 = 0$$

Solve for x

$$x=\frac{8\sqrt{3}}{3}+2\approx 6.618802154$$

$$x=-\frac{8\sqrt{3}}{3}+2\approx -2.618802154$$

Steps by Finding Square Root

Add 64 to both sides of the equation.

$$3\left(x-2\right)^{2}-64+64=64$$

Subtracting 64 from itself leaves 0.

$$3\left(x-2\right)^{2}=64$$

Divide both sides by 3.

$$\frac{3\left(x-2\right)^{2}}{3}=\frac{64}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$\left(x-2\right)^{2}=\frac{64}{3}$$

Take the square root of both sides of the equation.

$$x-2=\frac{8\sqrt{3}}{3} x-2=-\frac{8\sqrt{3}}{3}$$

Add 2 to both sides of the equation.

$$x-2-\left(-2\right)=\frac{8\sqrt{3}}{3}-\left(-2\right) x-2-\left(-2\right)=-\frac{8\sqrt{3}}{3}-\left(-2\right)$$

Subtracting -2 from itself leaves 0.

$$x=\frac{8\sqrt{3}}{3}-\left(-2\right) x=-\frac{8\sqrt{3}}{3}-\left(-2\right)$$

Subtract -2 from \frac{8\sqrt{3}}{3}.

$$x=\frac{8\sqrt{3}}{3}+2$$

Subtract -2 from -\frac{8\sqrt{3}}{3}.

$$x=-\frac{8\sqrt{3}}{3}+2$$

The equation is now solved.

$$x=\frac{8\sqrt{3}}{3}+2 x=-\frac{8\sqrt{3}}{3}+2$$