Let's solve the equation:

\[
x^2 + 11x + 29 = x + 4
\]

### Step 1: Move all terms to one side of the equation.
Subtract \(x + 4\) from both sides:

\[
x^2 + 11x + 29 - (x + 4) = 0
\]

Simplify the terms:

\[
x^2 + 11x - x + 29 - 4 = 0
\]

This reduces to:

\[
x^2 + 10x + 25 = 0
\]

### Step 2: Factor the quadratic equation.
Notice that the left-hand side is a perfect square trinomial:

\[
x^2 + 10x + 25 = (x + 5)^2
\]

### Step 3: Solve for \(x\).
Since \((x + 5)^2 = 0\), we can solve for \(x\):

\[
x + 5 = 0
\]

Thus:

\[
x = -5
\]

### Solution:
The solution to the equation is \(x = -5\).

Would you like more details or have any questions?

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Here are five related questions:
1. How do you solve a quadratic equation using the quadratic formula?
2. What is a perfect square trinomial, and how can it be identified?
3. Can all quadratic equations be factored, and if not, how are they solved?
4. How do you complete the square to solve quadratic equations?
5. What are the properties of solutions for quadratic equations?

**Tip:** Always check your solutions by substituting them back into the original equation to ensure correctness.

Learn how to solve the quadratic equation X² + 11x + 29 = x + 4 with a detailed step-by-step solution. The solution involves simplifying, factoring, and using the perfect square trinomial. Suitable for students in Grades 8-10.

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