1. Problem: No specific math problem was provided; I will demonstrate with a quick example to show how I can help fast. 2. Formula and important rules: To solve quadratic equations use the quadratic formula. $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ Rules: If $b^2 - 4ac > 0$ there are two distinct real roots. If $b^2 - 4ac = 0$ there is one real root (a repeated root). If $b^2 - 4ac < 0$ there are two complex conjugate roots. 3. Example problem: Solve $x^2 - 4 = 0$. 4. Intermediate work: Identify coefficients: $a = 1$, $b = 0$, $c = -4$. Compute the discriminant: $\Delta = b^2 - 4ac = 0^2 - 4 \cdot 1 \cdot (-4) = 16$. Evaluate square root: $\sqrt{\Delta} = \sqrt{16} = 4$. Apply the quadratic formula: $x = \frac{-b \pm \sqrt{\Delta}}{2a} = \frac{0 \pm 4}{2 \cdot 1} = \pm 2$. 5. Final answer: The solutions are $x = 2$ and $x = -2$. 6. How to get a fast, precise response: Provide the equation, specify desired steps, and indicate if you want numeric or symbolic answers. I am ready to solve your specific problem now.