Solving the Equation $9(x+9)^2=441$

To find the roots of the given equation, we first isolate the squared term:

1. Divide both sides by 9:

   $ (x+9)^2 = \frac{441}{9} $

   $ (x+9)^2 = 49 $

2. Take the square root of both sides. Remember to include both positive and negative roots:

   $ x+9 = \pm\sqrt{49} $

   $ x+9 = \pm 7 $

3. Solve for x in both cases:

   • Case 1 (Positive root):

     $ x + 9 = 7 $

     $ x = 7 - 9 $

     $ x = -2 $

   • Case 2 (Negative root):

     $ x + 9 = -7 $

     $ x = -7 - 9 $

     $ x = -16 $

Therefore, the roots of the equation $9(x+9)^2=441$ are -2 and -16.

Verification

The roots found are -2 and -16, which corresponds to Option D.