To solve the equation $x^2 - 6x - 25 = 0$ by completing the square, follow these steps:

Step-by-Step Process:

1. Move the constant term to the right side of the equation: $x^2 - 6x = 25$

2. Identify the coefficient of $x$ (which is -6), and divide it by 2, then square the result: $\left(\frac{-6}{2}\right)^2 = 9$

3. Add this square (9) to both sides of the equation to complete the square on the left-hand side: $x^2 - 6x + 9 = 25 + 9$

   Now, the left side becomes a perfect square trinomial.

4. Factor the left-hand side: $(x - 3)^2 = 34$

So, the correct step from the options provided is: $x^2 - 6x + 9 = 25 + 9$ This corresponds to option 1) in the image.

Would you like further details on completing the square?

Here are five related questions for further practice:

1. How do you complete the square for the equation $x^2 + 8x + 7 = 0$?
2. What is the geometric meaning of completing the square?
3. Can completing the square be used to solve any quadratic equation?
4. What is the relationship between completing the square and the quadratic formula?
5. How does completing the square help derive the vertex form of a parabola?

Tip: When completing the square, always remember to balance the equation by adding the same value to both sides.