Solve (x-4)^2=8

$$( x - 4 ) ^ { 2 } = 8$$

Solve for x

$$x=2\sqrt{2}+4\approx 6.828427125$$

$$x=4-2\sqrt{2}\approx 1.171572875$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$x-4=2\sqrt{2} x-4=-2\sqrt{2}$$

Add 4 to both sides of the equation.

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

Subtracting -4 from itself leaves 0.

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

Subtract -4 from 2\sqrt{2}.

$$x=2\sqrt{2}+4$$

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

$$x=4-2\sqrt{2}$$

The equation is now solved.

$$x=2\sqrt{2}+4 x=4-2\sqrt{2}$$