Solve 2(x-2)^2-4=0

$$2 ( x - 2 ) ^ { 2 } - 4 = 0$$

Solve for x

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

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

Steps by Finding Square Root

Add 4 to both sides of the equation.

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

Subtracting 4 from itself leaves 0.

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

Divide both sides by 2.

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

Dividing by 2 undoes the multiplication by 2.

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

Divide 4 by 2.

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

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.

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