(x-2)2-9=0

Add 9 to both sides of the equation.

(x-2)2=9

Take the square root of each side of the equation to set up the solution for x

(x-2)2⋅12=±9

Remove the perfect root factor x-2 under the radical to solve for x.

x-2=±9

Rewrite 9 as 32.

x-2=±32

Pull terms out from under the radical, assuming positive real numbers.

x-2=±3

x-2=±3

First, use the positive value of the ± to find the first solution.

x-2=3

Move all terms not containing x to the right side of the equation.

Add 2 to both sides of the equation.

x=3+2

Add 3 and 2.

x=5

x=5

Next, use the negative value of the ± to find the second solution.

x-2=-3

Move all terms not containing x to the right side of the equation.

Add 2 to both sides of the equation.

x=-3+2

Add -3 and 2.

x=-1

x=-1

The complete solution is the result of both the positive and negative portions of the solution.

x=5,-1

x=5,-1

Solve Using the Square Root Property (x-2)^2-9=0