Final answer:
To solve a quadratic equation of the form ax² + bx + c = 0, we use the quadratic formula. The solutions provided are potential values for x. We must verify these solutions by substituting them back into the original equation to ensure they are correct.
Step-by-step explanation:
Solving Quadratic Equations
When given a quadratic equation in the form ax² + bx + c = 0, we can solve for the variable x by using the quadratic formula. This formula is √x = (-b ± √(b² - 4ac)) / (2a), where a, b, and c are constants. In this scenario, you've provided various solutions to an unspecified original equation, but it appears to involve solving for x using the quadratic formula. After finding the discriminant, b² - 4ac, we assess whether we have two, one or no real solution(s), and then we identify the correct values of x using both the + and - signs in the formula.
For each original equation, we would substitute our given values for a, b, and c into the quadratic formula to find the potential values for x. As per the presented options, we must also consider the context of the problem to determine which solution makes sense, as sometimes one value may be physically impossible or irrelevant given real-world constraints, and therefore can be discarded.
In the context of your provided answers, if these are derived from a possible quadratic equation, you should verify the solutions by substituting them back into the original equation to see if they satisfy it. This process of verification is essential to determine the correct solutions and discard any that do not fit the established conditions of the problem.