Solve (y-4)^2-72=0

$$( y - 4 ) ^ { 2 } - 72 = 0$$

Solve for y

$$y=6\sqrt{2}+4\approx 12.485281374$$

$$y=4-6\sqrt{2}\approx -4.485281374$$

Steps by Finding Square Root

Add 72 to both sides of the equation.

$$\left(y-4\right)^{2}-72+72=72$$

Subtracting 72 from itself leaves 0.

$$\left(y-4\right)^{2}=72$$

Take the square root of both sides of the equation.

$$y-4=6\sqrt{2} y-4=-6\sqrt{2}$$

Add 4 to both sides of the equation.

$$y-4-\left(-4\right)=6\sqrt{2}-\left(-4\right) y-4-\left(-4\right)=-6\sqrt{2}-\left(-4\right)$$

Subtracting -4 from itself leaves 0.

$$y=6\sqrt{2}-\left(-4\right) y=-6\sqrt{2}-\left(-4\right)$$

Subtract -4 from 6\sqrt{2}.

$$y=6\sqrt{2}+4$$

Subtract -4 from -6\sqrt{2}.

$$y=4-6\sqrt{2}$$

The equation is now solved.

$$y=6\sqrt{2}+4 y=4-6\sqrt{2}$$