What number should be added to both sides of the equation x² + 12x – 11 to complete the square?

To complete the square for the quadratic equation x² + 12x – 11, we need to focus on the quadratic and linear terms, which are x² + 12x.

Here’s a step-by-step process to determine the number to add:

1. Take the coefficient of the linear term (which is 12 in this case) and divide it by 2:
   12 / 2 = 6
2. Next, square this result:
   6² = 36

So, to complete the square, we need to add 36 to both sides of the equation.

The transformed equation would be:

x² + 12x + 36 – 11 = 36

This simplifies to:

(x + 6)² – 11 = 36

In summary, to complete the square for the equation x² + 12x – 11, the number you should add to both sides is 36.