Solve 2(x-2)^2-36=0

$$2 ( x - 2 ) ^ { 2 } - 36 = 0$$

Solve for x

$$x=3\sqrt{2}+2\approx 6.242640687$$

$$x=2-3\sqrt{2}\approx -2.242640687$$

Steps by Finding Square Root

Add 36 to both sides of the equation.

$$2\left(x-2\right)^{2}-36+36=36$$

Subtracting 36 from itself leaves 0.

$$2\left(x-2\right)^{2}=36$$

Divide both sides by 2.

$$\frac{2\left(x-2\right)^{2}}{2}=\frac{36}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$\left(x-2\right)^{2}=\frac{36}{2}$$

Divide 36 by 2.

$$\left(x-2\right)^{2}=18$$

Take the square root of both sides of the equation.

$$x-2=3\sqrt{2} x-2=-3\sqrt{2}$$

Add 2 to both sides of the equation.

$$x-2-\left(-2\right)=3\sqrt{2}-\left(-2\right) x-2-\left(-2\right)=-3\sqrt{2}-\left(-2\right)$$

Subtracting -2 from itself leaves 0.

$$x=3\sqrt{2}-\left(-2\right) x=-3\sqrt{2}-\left(-2\right)$$

Subtract -2 from 3\sqrt{2}.

$$x=3\sqrt{2}+2$$

Subtract -2 from -3\sqrt{2}.

$$x=2-3\sqrt{2}$$

The equation is now solved.

$$x=3\sqrt{2}+2 x=2-3\sqrt{2}$$