What number should be added to both sides of the equation to complete the square x² + 10x – 7?

To complete the square for the expression x² + 10x – 7, we need to focus on the quadratic part, which is x² + 10x.

First, we take the coefficient of the x term, which is 10, divide it by 2, and then square the result. Here are the steps:

1. Take the coefficient of x: 10.
2. Divide it by 2: 10 / 2 = 5.
3. Square that result: 5² = 25.

Now, to complete the square, we add this number (25) to both sides of the equation. So we rewrite the equation as:

x² + 10x + 25 = 7 + 25.

This simplifies to:

(x + 5)² = 32.

Therefore, the number that should be added to both sides of the equation to complete the square is 25.