Final answer:
An equation with a squared variable often provides two solutions, but not all may be applicable or meaningful, referred to as extraneous solutions. To check, you have to substitute the proposed solutions back into the original equation to see if they satisfy the equation.
Step-by-step explanation:
In mathematics, an equation with an unknown variable squared will indeed present two solutions. You know these as the positives and negatives typically resulting from the solutions to quadratic equations. Nonetheless, it's important to note that not both solutions may be meaningful or applicable in the context of a question or scenario. We refer these non-meaningful or irrelevant solutions as extraneous solutions.
If the solutions x = 8 and x = 1 were proposed for an equation that's not presented in the question, it's hard to definitively say whether either of these solutions are extraneous. What we need to do is to substitute these values back into the original equation. If both values satisfy the equation, then neither solution is extraneous. However, if substituting any of these values into the equation results in an untrue statement, then that particular solution is extraneous.
Learn more about Extraneous Solutions