1. **State the problem:** Solve the quadratic equation $$x^2 - 8x = -15$$. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero: $$x^2 - 8x + 15 = 0$$ 3. **Identify coefficients:** Here, $$a = 1$$, $$b = -8$$, and $$c = 15$$. 4. **Use the quadratic formula:** $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ 5. **Calculate the discriminant:** $$b^2 - 4ac = (-8)^2 - 4 \times 1 \times 15 = 64 - 60 = 4$$ 6. **Calculate the roots:** $$x = \frac{-(-8) \pm \sqrt{4}}{2 \times 1} = \frac{8 \pm 2}{2}$$ 7. **Find the two solutions:** $$x_1 = \frac{8 + 2}{2} = \frac{10}{2} = 5$$ $$x_2 = \frac{8 - 2}{2} = \frac{6}{2} = 3$$ **Final answer:** $$x = 5$$ or $$x = 3$$.