1. **State the problem:** Complete the square for the quadratic equation $$x^2 - 8x = 10$$ given constants $$A=13$$ and $$C=-20$$. 2. **Recall the formula for completing the square:** For an equation of the form $$x^2 + bx = c$$, we add and subtract $$\left(\frac{b}{2}\right)^2$$ to complete the square: $$x^2 + bx + \left(\frac{b}{2}\right)^2 = c + \left(\frac{b}{2}\right)^2$$ 3. **Identify coefficients:** Here, $$b = -8$$. 4. **Calculate $$\left(\frac{b}{2}\right)^2$$:** $$\left(\frac{-8}{2}\right)^2 = (-4)^2 = 16$$ 5. **Add and subtract 16 to the left side:** $$x^2 - 8x + 16 - 16 = 10$$ 6. **Group the perfect square trinomial:** $$\left(x^2 - 8x + 16\right) - 16 = 10$$ 7. **Rewrite as a square:** $$\left(x - 4\right)^2 - 16 = 10$$ 8. **Isolate the perfect square:** $$\left(x - 4\right)^2 = 10 + 16$$ $$\left(x - 4\right)^2 = 26$$ 9. **Final completed square form:** $$\boxed{\left(x - 4\right)^2 = 26}$$ Note: Constants $$A=13$$ and $$C=-20$$ are not directly used in completing the square for this equation but may relate to a larger context or different problem.