(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

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

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