Solve (v-6)^2-72=0

$$( v - 6 ) ^ { 2 } - 72 = 0$$

Solve for v

$$v=6\sqrt{2}+6\approx 14.485281374$$

$$v=6-6\sqrt{2}\approx -2.485281374$$

Steps by Finding Square Root

Add 72 to both sides of the equation.

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

Subtracting 72 from itself leaves 0.

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

Take the square root of both sides of the equation.

$$v-6=6\sqrt{2} v-6=-6\sqrt{2}$$

Add 6 to both sides of the equation.

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

Subtracting -6 from itself leaves 0.

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

Subtract -6 from 6\sqrt{2}.

$$v=6\sqrt{2}+6$$

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

$$v=6-6\sqrt{2}$$

The equation is now solved.

$$v=6\sqrt{2}+6 v=6-6\sqrt{2}$$