Solve 6left(x-7right)^2-72=0

$$6 { \left(x-7 \right) }^{ 2 } -72 = 0$$

Solve for x

$$x=2\sqrt{3}+7\approx 10.464101615$$

$$x=7-2\sqrt{3}\approx 3.535898385$$

Steps by Finding Square Root

Add 72 to both sides of the equation.

$$6\left(x-7\right)^{2}-72+72=72$$

Subtracting 72 from itself leaves 0.

$$6\left(x-7\right)^{2}=72$$

Divide both sides by 6.

$$\frac{6\left(x-7\right)^{2}}{6}=\frac{72}{6}$$

Dividing by 6 undoes the multiplication by 6.

$$\left(x-7\right)^{2}=\frac{72}{6}$$

Divide 72 by 6.

$$\left(x-7\right)^{2}=12$$

Take the square root of both sides of the equation.

$$x-7=2\sqrt{3} x-7=-2\sqrt{3}$$

Add 7 to both sides of the equation.

$$x-7-\left(-7\right)=2\sqrt{3}-\left(-7\right) x-7-\left(-7\right)=-2\sqrt{3}-\left(-7\right)$$

Subtracting -7 from itself leaves 0.

$$x=2\sqrt{3}-\left(-7\right) x=-2\sqrt{3}-\left(-7\right)$$

Subtract -7 from 2\sqrt{3}.

$$x=2\sqrt{3}+7$$

Subtract -7 from -2\sqrt{3}.

$$x=7-2\sqrt{3}$$

The equation is now solved.

$$x=2\sqrt{3}+7 x=7-2\sqrt{3}$$