It seems like you want to find the value of \( x \) for the expression \( x^{2} - 6x - 55 = 0 \).

To solve this quadratic equation, we’ll use the factoring method:

1. **Rewrite the equation**: 
   \[
   x^{2} - 6x - 55 = 0
   \]

2. **Find two numbers that multiply to -55 and add up to -6**: 
   - The numbers -11 and 5 satisfy these conditions because:
     \[
     -11 \times 5 = -55 \quad \text{and} \quad -11 + 5 = -6
     \]

3. **Rewrite the middle term using these numbers**: 
   \[
   x^{2} - 11x + 5x - 55 = 0
   \]

4. **Factor by grouping**: 
   \[
   x(x - 11) + 5(x - 11) = 0
   \]

5. **Factor out \( x - 11 \)**:
   \[
   (x - 11)(x + 5) = 0
   \]

6. **Set each factor to zero**:
   - \( x - 11 = 0 \) or \( x + 5 = 0 \)
   - Solving these gives:
     \[
     x = 11 \quad \text{or} \quad x = -5
     \]

### Solution
The values of \( x \) that satisfy the equation \( x^{2} - 6x - 55 = 0 \) are:
\[
x = 11 \quad \text{and} \quad x = -5
\]

Would you like more details on this solution?

---

1. How is the quadratic formula applied to solve \( x^2 - 6x - 55 = 0 \)?
2. What other methods could solve this quadratic equation?
3. What are the steps for verifying the solutions for \( x = 11 \) and \( x = -5 \)?
4. Can complex solutions appear in similar quadratic equations?
5. How does completing the square solve \( x^2 - 6x - 55 = 0 \)?

**Tip**: Always check your solutions by plugging them back into the original equation.

Learn how to solve the quadratic equation x^2 - 6x - 55 by factoring. Follow the step-by-step solution to find the values of x, utilizing key algebraic concepts such as factoring and the Zero Product Property. Suitable for students in Grades 8-10.

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