Solve (x-2)^2+1=12

$$( x - 2 ) ^ { 2 } + 1 = 12$$

Solve for x

$$x=\sqrt{11}+2\approx 5.31662479$$

$$x=2-\sqrt{11}\approx -1.31662479$$

Steps by Finding Square Root

Subtract 1 from both sides of the equation.

$$\left(x-2\right)^{2}+1-1=12-1$$

Subtracting 1 from itself leaves 0.

$$\left(x-2\right)^{2}=12-1$$

Subtract 1 from 12.

$$\left(x-2\right)^{2}=11$$

Take the square root of both sides of the equation.

$$x-2=\sqrt{11} x-2=-\sqrt{11}$$

Add 2 to both sides of the equation.

$$x-2-\left(-2\right)=\sqrt{11}-\left(-2\right) x-2-\left(-2\right)=-\sqrt{11}-\left(-2\right)$$

Subtracting -2 from itself leaves 0.

$$x=\sqrt{11}-\left(-2\right) x=-\sqrt{11}-\left(-2\right)$$

Subtract -2 from \sqrt{11}.

$$x=\sqrt{11}+2$$

Subtract -2 from -\sqrt{11}.

$$x=2-\sqrt{11}$$

The equation is now solved.

$$x=\sqrt{11}+2 x=2-\sqrt{11}$$