1. **State the problem:** Solve the quadratic equation $$x^2 + (8.8 \times 10^{-6})x - (3.96 \times 10^{-7}) = 0.$$\n\n2. **Formula used:** The quadratic formula for an equation $$ax^2 + bx + c = 0$$ is $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.$$ Here, $$a=1$$, $$b=8.8 \times 10^{-6}$$, and $$c = -3.96 \times 10^{-7}$$.\n\n3. **Calculate the discriminant:** $$\Delta = b^2 - 4ac = (8.8 \times 10^{-6})^2 - 4 \times 1 \times (-3.96 \times 10^{-7}) = 7.744 \times 10^{-11} + 1.584 \times 10^{-6} = 1.58407744 \times 10^{-6}.$$\n\n4. **Calculate the square root of the discriminant:** $$\sqrt{\Delta} = \sqrt{1.58407744 \times 10^{-6}} \approx 0.0012586.$$\n\n5. **Apply the quadratic formula:**\n$$x = \frac{-(8.8 \times 10^{-6}) \pm 0.0012586}{2}.$$\n\n6. **Calculate each root:**\n- For the plus sign:\n$$x_1 = \frac{-8.8 \times 10^{-6} + 0.0012586}{2} = \frac{0.0012498}{2} = 0.0006249.$$\n- For the minus sign:\n$$x_2 = \frac{-8.8 \times 10^{-6} - 0.0012586}{2} = \frac{-0.0012674}{2} = -0.0006337.$$\n\n7. **Final answer:** The solutions to the quadratic equation are $$x \approx 6.249 \times 10^{-4}$$ and $$x \approx -6.337 \times 10^{-4}.$$