# Solve for z (z-2)^2=-36 (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
Simplify the right side of the equation.
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
The complete solution is the result of both the positive and negative portions of the solution.
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

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