(z-2)2=-36

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

(z-2)2⋅12=±-36

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

z-2=±-36

Rewrite -36 as -1(36).

z-2=±-1⋅36

Rewrite -1(36) as -1⋅36.

z-2=±-1⋅36

Rewrite -1 as i.

z-2=±i⋅36

Rewrite 36 as 62.

z-2=±i⋅62

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

z-2=±i⋅6

Move 6 to the left of i.

z-2=±6i

z-2=±6i

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

z-2=6i

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

Add 2 to both sides of the equation.

z=6i+2

Reorder 6i and 2.

z=2+6i

z=2+6i

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

z-2=-6i

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

Add 2 to both sides of the equation.

z=-6i+2

Reorder -6i and 2.

z=2-6i

z=2-6i

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

z=2+6i,2-6i

z=2+6i,2-6i

Solve for z (z-2)^2=-36