Solve (x-2)^2=2

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

Solve for x

$$x=\sqrt{2}+2\approx 3.414213562$$

$$x=2-\sqrt{2}\approx 0.585786438$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

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

Add 2 to both sides of the equation.

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

Subtracting -2 from itself leaves 0.

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

Subtract -2 from \sqrt{2}.

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

Subtract -2 from -\sqrt{2}.

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

The equation is now solved.

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