Question: You are trying to solve the quadratic equation $x^2 + 8x = -5$.
After completing the square, which of the following is the resulting equation?
$x^2 + 8x - 16 = -21$
$x^2 + 8x - 64 = -69$
$x^2 + 8x + 16 = 11$
$x^2 + 8x + 64 = 59$
1. **State the problem:** We want to solve the quadratic equation $$x^2 + 8x = -5$$ by completing the square.
2. **Recall the formula for completing the square:** For an equation of the form $$x^2 + bx = c$$, we add $$\left(\frac{b}{2}\right)^2$$ to both sides to form a perfect square trinomial on the left.
3. **Calculate the term to add:** Here, $$b = 8$$, so
$$\left(\frac{8}{2}\right)^2 = 4^2 = 16$$
4. **Add 16 to both sides:**
$$x^2 + 8x + 16 = -5 + 16$$
5. **Simplify the right side:**
$$x^2 + 8x + 16 = 11$$
6. **Result:** The equation after completing the square is
$$x^2 + 8x + 16 = 11$$
This matches the third option.
**Final answer:** $$x^2 + 8x + 16 = 11$$