Solve 2(x-3)^2=16

$$2 ( x - 3 ) ^ { 2 } = 16$$

Solve for x

$$x=2\sqrt{2}+3\approx 5.828427125$$

$$x=3-2\sqrt{2}\approx 0.171572875$$

Steps by Finding Square Root

Divide both sides by 2.

$$\frac{2\left(x-3\right)^{2}}{2}=\frac{16}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$\left(x-3\right)^{2}=\frac{16}{2}$$

Divide 16 by 2.

$$\left(x-3\right)^{2}=8$$

Take the square root of both sides of the equation.

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

Add 3 to both sides of the equation.

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

Subtracting -3 from itself leaves 0.

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

Subtract -3 from 2\sqrt{2}.

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

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

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

The equation is now solved.

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