To complete the square for the equation x² + 12x – 11, we first focus on the quadratic part, which is x² + 12x.
To find the number that needs to be added, we take the coefficient of x, which is 12, divide it by 2, and then square the result. Here’s the calculation:
- 12 ÷ 2 = 6
- 6² = 36
So, we need to add 36. However, since this is being added to both sides of the equation, we also need to adjust the constant term on the left side. The original equation is:
x² + 12x – 11 = 0
If we add 36 to both sides, we adjust it as follows:
x² + 12x + 36 – 11 – 36 = 0 + 36
This simplifies to:
(x + 6)² – 47 = 36
Thus, to complete the square in the equation x² + 12x – 11, we should add 36 to both sides.