To solve the equation \( (x - 9)^2 - 44 = 0 \), follow these steps:

### Step 1: Isolate the squared term
Add 44 to both sides to eliminate the constant on the left side:

\[
(x - 9)^2 = 44
\]

### Step 2: Take the square root of both sides
To solve for \(x - 9\), take the square root of both sides. Remember to account for both the positive and negative square roots:

\[
x - 9 = \pm \sqrt{44}
\]

Since \( \sqrt{44} = \sqrt{4 \times 11} = 2\sqrt{11} \), we get:

\[
x - 9 = \pm 2\sqrt{11}
\]

### Step 3: Solve for \(x\)
Now, add 9 to both sides to solve for \(x\):

\[
x = 9 \pm 2\sqrt{11}
\]

Thus, the solutions are:

\[
x = 9 + 2\sqrt{11} \quad \text{or} \quad x = 9 - 2\sqrt{11}
\]

These are the two solutions in exact form.

Would you like further details or clarifications?

Here are some related questions:
1. How do you simplify square roots with factors?
2. What are the properties of quadratic equations?
3. How can we approximate \( \sqrt{11} \) numerically?
4. What is the general method for solving quadratic equations?
5. Can you explain how squaring both sides affects equations?

**Tip:** Always check both the positive and negative roots when solving equations with squares!

Learn how to solve the quadratic equation (x-9)^2 - 44 = 0 using square roots and algebraic manipulation. Follow a step-by-step guide to isolate the variable and find the exact solutions for x. This problem involves quadratic equations and square roots, suitable for students in Grades 9-10.

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