We start with the given equation:

\[
(x + 2)^2 + (9 - 1)^2 = 4
\]

Let's break it down step by step:

### Step 1: Simplify the terms

First, simplify the constants within the equation:

\[
(9 - 1)^2 = 8^2 = 64
\]

Now, the equation becomes:

\[
(x + 2)^2 + 64 = 4
\]

### Step 2: Isolate \((x + 2)^2\)

Next, subtract 64 from both sides of the equation:

\[
(x + 2)^2 = 4 - 64
\]

Simplifying further:

\[
(x + 2)^2 = -60
\]

### Step 3: Analyze the result

At this point, we have:

\[
(x + 2)^2 = -60
\]

Since the square of any real number cannot be negative, this equation has no real solutions for \(x\). Therefore, **no real value** of \(x\) satisfies this equation.

### Nilal \(m = 3\)

It seems you mentioned that \(m = 3\), but it's unclear how \(m\) relates to the equation. Could you clarify its role? 

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Would you like to explore any part of this explanation in more detail? 

Here are 5 follow-up questions based on this content:

1. What happens if we solve \((x + 2)^2 = -60\) in the complex number system?
2. How do we generally handle equations with no real solutions?
3. What are some examples of quadratic equations with complex solutions?
4. Can you solve equations like \((x + 2)^2 = k\) for any constant \(k\)?
5. How can you verify if an equation has real or complex solutions?

**Tip:** Always check the sign of an expression like \((x + a)^2\); if it's negative, expect complex solutions.

Explore the steps to solve the quadratic equation (x + 2)² + 8² = 4. This problem involves algebraic manipulation and understanding complex number solutions. Learn why there are no real solutions for x in this equation. Suitable for students in Grades 9-11.

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