The equation provided is $x^2 + 8x - 5 = 0$, and it asks for solving it by completing the square. Let me solve this step by step:

Steps to Solve by Completing the Square:

1. Rearrange the equation:
   Move the constant term (-5) to the other side:
   $x^2 + 8x = 5$

2. Complete the square:
   Take half of the coefficient of $x$ (which is $8$), square it, and add it to both sides.
   Half of $8$ is $4$, and $4^2 = 16$.
   Add $16$ to both sides:
   $x^2 + 8x + 16 = 5 + 16$ Simplify:
   $(x + 4)^2 = 21$

3. Solve for $x$:
   Take the square root of both sides:
   $x + 4 = \pm\sqrt{21}$

4. Isolate $x$:
   Subtract $4$ from both sides:
   $x = -4 \pm \sqrt{21}$

Final Answer:

The solutions are:
$x = -4 + \sqrt{21}, \, x = -4 - \sqrt{21}$

Would you like a more detailed explanation, or do you have any questions?

Related Questions:

1. What are the steps to solve quadratic equations using the quadratic formula?
2. How can completing the square help in graphing parabolas?
3. What are some real-life applications of solving quadratic equations?
4. Can all quadratic equations be solved by completing the square?
5. What is the relationship between completing the square and vertex form?

Tip: Completing the square is useful for rewriting quadratics in vertex form, which is great for identifying the maximum or minimum points!