(n-9)2=-4

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

(n-9)2⋅12=±-4

Remove the perfect root factor n-9 under the radical to solve for n.

n-9=±-4

Rewrite -4 as -1(4).

n-9=±-1⋅4

Rewrite -1(4) as -1⋅4.

n-9=±-1⋅4

Rewrite -1 as i.

n-9=±i⋅4

Rewrite 4 as 22.

n-9=±i⋅22

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

n-9=±i⋅2

Move 2 to the left of i.

n-9=±2i

n-9=±2i

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

n-9=2i

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

Add 9 to both sides of the equation.

n=2i+9

Reorder 2i and 9.

n=9+2i

n=9+2i

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

n-9=-2i

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

Add 9 to both sides of the equation.

n=-2i+9

Reorder -2i and 9.

n=9-2i

n=9-2i

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

n=9+2i,9-2i

n=9+2i,9-2i

Solve using the Square Root Property (n-9)^2=-4