Final answer:
The general solution to a quadratic equation ax² + bx + c = 0 is found using the quadratic formula x = (-b ± √(b² - 4ac))/(2a), resulting in two possible values for x, one of which may be discarded based on the context of the problem.
Step-by-step explanation:
To solve a quadratic equation of the form ax² + bx + c = 0, one can apply the quadratic formula, which is x = (-b ± √(b² - 4ac))/(2a). This formula will provide the two possible solutions for x. When using this formula, it is important to consider the context of the problem since a negative result may not make sense in a real-world scenario. Moreover, some special cases like a cubic equation cannot be solved using the quadratic formula, and other methods such as graphing or numerical approaches may be used.
For example, if we have an equation x² + 0.0211x - 0.0211 = 0, applying the quadratic formula would yield two possible solutions for x. We would substitute a = 1, b = 0.0211, and c = -0.0211 into the formula to find the values of x.