How do you solve x² + 8x + 5 = 0 using the completing the square method?

To solve the quadratic equation x² + 8x + 5 = 0 by completing the square, follow these steps:

1. Start with the original equation:

x² + 8x + 5 = 0

2. Move the constant to the other side of the equation:

x² + 8x = -5

3. To complete the square, take the coefficient of x (which is 8), divide it by 2, and square it:

(8 / 2)² = 4² = 16

4. Add this square to both sides of the equation:

x² + 8x + 16 = -5 + 16

This simplifies to:

x² + 8x + 16 = 11

Now, the left side can be factored as a perfect square:

(x + 4)² = 11

1. Take the square root of both sides:

x + 4 = ±√11

2. Now, solve for x by isolating the variable:

x = -4 ± √11

Thus, the solutions are:

x = -4 + √11 and x = -4 – √11.