Final answer:
To solve a quadratic equation, we can factor, complete the square, or use the quadratic formula. Only one of the possible solutions may be valid depending on the context of the problem. The correct method depends on the specific form and details of the equation.
Step-by-step explanation:
To solve for x in the given equation, we need to follow a step-by-step approach. The details and calculations involved in the provided examples suggest that we're often dealing with a quadratic equation, which might require manipulation into the standard quadratic form and then solving either by factoring, completing the square, or using the quadratic formula. However, without a specific equation or set of conditions provided in the question, we can't provide a detailed solution. In one instance, if the equation is set to zero and appears to be a perfect square, factoring would be the easiest method. In another example, assuming that x is much smaller than a given constant could simplify the equation and allow for straightforward solving.
When applying the quadratic formula, we calculate two potential values for x and then interpret them within the context of the problem. Often, only one of the solutions will be physically or contextually plausible, and the other should be discarded. An example in the information provided shows that one of the computed values of x was negative, which didn't make sense in the given real-life context, so the positive value was accepted as the true solution.