Final answer:
When an equation involves square roots and yields two solutions, both the positive and negative solutions are generally valid. However, context matters, and depending on the problem, negative solutions may not make sense and could be discarded.
Step-by-step explanation:
When solving an equation that involves an unknown squared, resulting in square roots, it is possible to end up with two solutions: one positive and one negative. In many cases, both solutions should be included because they are mathematically valid. However, depending on the context of the problem, you may need to consider which solution makes sense. For instance, if you are dealing with lengths or distances, negative solutions may be discarded as they do not represent real-world measurements. Equations that involve physical quantities often have only one reasonable solution that fits within the context of the problem.
For equations not constrained by physical realities, such as pure mathematics problems, both the positive solution and negative solution are valid and should be considered. Always make sure to understand the context of the problem and use logical reasoning to determine whether to include or discard a solution. It is also necessary to know how to perform operations such as taking square roots or cube roots on a calculator for correct computation.