The given equation is:

\[
(x + 2)^2 - 9 = 9
\]

First, add 9 to both sides to simplify the equation:

\[
(x + 2)^2 = 9 + 9
\]

\[
(x + 2)^2 = 18
\]

Next, take the square root of both sides:

\[
x + 2 = \pm \sqrt{18}
\]

Simplify \(\sqrt{18}\):

\[
\sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2} = 3\sqrt{2}
\]

So the equation becomes:

\[
x + 2 = \pm 3\sqrt{2}
\]

Finally, subtract 2 from both sides to solve for \( x \):

\[
x = -2 \pm 3\sqrt{2}
\]

Therefore, the solutions are:

\[
x = -2 + 3\sqrt{2}, \quad x = -2 - 3\sqrt{2}
\]

Would you like more details or have any questions?

Here are 5 related questions for further practice:
1. Solve \((x - 3)^2 - 16 = 0\).
2. What are the solutions to the equation \((x + 1)^2 = 25\)?
3. Solve \((x - 5)^2 - 4 = 20\).
4. What are the roots of the quadratic equation \((x + 4)^2 - 9 = 0\)?
5. Solve \((x - 2)^2 - 25 = 16\) and simplify your answer.

**Tip:** Always remember to apply the square root to both positive and negative values when solving quadratic equations of the form \((x + a)^2 = b\).

Learn how to solve the quadratic equation (x + 2)^2 - 9 = 9 with a step-by-step solution. This problem involves quadratic equations and square roots, covering essential algebraic concepts. Suitable for students in Grades 9-12.

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