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The equation provided is:

\[
x^2 - 6x - 5 = (x - \_ )^2 - \_
\]

This problem is asking us to complete the square. Here's the step-by-step solution:

1. Start with the quadratic term and the linear term: \(x^2 - 6x\).
   
2. To complete the square, we take half of the coefficient of \(x\), which is \(-6\), divide it by 2, and then square it.
   
   \[
   \frac{-6}{2} = -3 \quad \text{and} \quad (-3)^2 = 9
   \]
   
3. So, we rewrite \(x^2 - 6x\) as \( (x - 3)^2 - 9 \) to complete the square.

4. Now, rewrite the full expression, keeping in mind that the original constant term was \(-5\):
   \[
   x^2 - 6x - 5 = (x - 3)^2 - 9 - 5
   \]
   
5. Simplify the constants on the right side:
   \[
   (x - 3)^2 - 9 - 5 = (x - 3)^2 - 14
   \]

Thus, the completed square form of the equation is:

\[
x^2 - 6x - 5 = (x - 3)^2 - 14
\]

The missing numbers in the equation are **3** and **14**.

---

Do you need further details or have any questions?

Here are some related questions to explore:

1. How would you complete the square for \(x^2 + 8x - 7\)?
2. Can you solve quadratic equations by completing the square?
3. How does completing the square help in finding the vertex of a parabola?
4. What is the relationship between completing the square and the quadratic formula?
5. How can you apply completing the square to solve quadratic inequalities?

**Tip**: When completing the square, always remember to balance the equation by adding and subtracting the same value on both sides!

Fill in the gaps in the equation below by completing the square: x^2 - 6x - 5 = (x - __)^2 - __.

Learn how to complete the square for the equation x^2 - 6x - 5 and find the missing values. This step-by-step guide covers key algebraic concepts suitable for students in Grades 8-10.

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