How do you solve x² + 12x + 11 by completing the square?

To solve the quadratic equation x² + 12x + 11 = 0 by completing the square, we start by rearranging the equation:

x² + 12x + 11 = 0 can be rewritten as x² + 12x = -11.

Next, we need to complete the square on the left side. To do this, we take the coefficient of x, which is 12, divide it by 2 (getting 6), and then square it (resulting in 36).

We add and subtract 36 in the equation:

x² + 12x + 36 – 36 = -11

This simplifies to:

(x + 6)² – 36 = -11

Now, we can isolate the square:

(x + 6)² = 36 – 11

Which further simplifies to:

(x + 6)² = 25

Now we can take the square root of both sides:

x + 6 = ±5

This gives us two equations to solve:

1. x + 6 = 5 → x = -1
2. x + 6 = -5 → x = -11

Thus, the solution set of the equation is:

{ -1, -11 }