# Solve for z (z+9)^2=-49 (z+9)2=-49
Take the square root of each side of the equation to set up the solution for z
(z+9)2⋅12=±-49
Remove the perfect root factor z+9 under the radical to solve for z.
z+9=±-49
Simplify the right side of the equation.
Rewrite -49 as -1(49).
z+9=±-1⋅49
Rewrite -1(49) as -1⋅49.
z+9=±-1⋅49
Rewrite -1 as i.
z+9=±i⋅49
Rewrite 49 as 72.
z+9=±i⋅72
Pull terms out from under the radical, assuming positive real numbers.
z+9=±i⋅7
Move 7 to the left of i.
z+9=±7i
z+9=±7i
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+9=7i
Move all terms not containing z to the right side of the equation.
Subtract 9 from both sides of the equation.
z=7i-9
Reorder 7i and -9.
z=-9+7i
z=-9+7i
Next, use the negative value of the ± to find the second solution.
z+9=-7i
Move all terms not containing z to the right side of the equation.
Subtract 9 from both sides of the equation.
z=-7i-9
Reorder -7i and -9.
z=-9-7i
z=-9-7i
The complete solution is the result of both the positive and negative portions of the solution.
z=-9+7i,-9-7i
z=-9+7i,-9-7i
Solve for z (z+9)^2=-49

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