1. The problem is to find the solutions of a quadratic equation of the form $ax^2 + bx + c = 0$. 2. The quadratic formula used to solve this is: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ 3. Important rules: - The term under the square root, $b^2 - 4ac$, is called the discriminant. - If the discriminant is positive, there are two real solutions. - If it is zero, there is one real solution. - If it is negative, there are two complex solutions. 4. To use the formula, identify $a$, $b$, and $c$ from your quadratic equation. 5. Calculate the discriminant $\Delta = b^2 - 4ac$. 6. Substitute $a$, $b$, and $\Delta$ into the formula and simplify to find the values of $x$. This formula gives the roots of any quadratic equation.