Solve left(x-5right)^2-72=0

$${ \left(x-5 \right) }^{ 2 } -72=0$$

Solve for x

$$x=6\sqrt{2}+5\approx 13.485281374$$

$$x=5-6\sqrt{2}\approx -3.485281374$$

Steps by Finding Square Root

Add 72 to both sides of the equation.

$$\left(x-5\right)^{2}-72+72=72$$

Subtracting 72 from itself leaves 0.

$$\left(x-5\right)^{2}=72$$

Take the square root of both sides of the equation.

$$x-5=6\sqrt{2} x-5=-6\sqrt{2}$$

Add 5 to both sides of the equation.

$$x-5-\left(-5\right)=6\sqrt{2}-\left(-5\right) x-5-\left(-5\right)=-6\sqrt{2}-\left(-5\right)$$

Subtracting -5 from itself leaves 0.

$$x=6\sqrt{2}-\left(-5\right) x=-6\sqrt{2}-\left(-5\right)$$

Subtract -5 from 6\sqrt{2}.

$$x=6\sqrt{2}+5$$

Subtract -5 from -6\sqrt{2}.

$$x=5-6\sqrt{2}$$

The equation is now solved.

$$x=6\sqrt{2}+5 x=5-6\sqrt{2}$$