# Solve using the Square Root Property (n-9)^2=-4 (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
Simplify the right side of the equation.
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
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.
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
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