Final answer:
The value of x is determined by solving a quadratic equation and considering the sign rules for multiplication to evaluate the possible solutions. In many cases, only one solution is practical and thus chosen as the correct answer.
Step-by-step explanation:
The question involves solving a quadratic equation to find the value of x. To solve the equation, we first set it equal to zero and then use the quadratic formula. The examples provided suggest that, after rearranging the terms into a standard quadratic form, we can apply the quadratic formula to find two possible solutions for x. In real-world situations, only one of these solutions may be practical or make sense, so the other can be discarded as physically impossible.
Sign rules for multiplication indicate that when two numbers with the same sign are multiplied, the result is positive, while multiplication of two numbers with opposite signs results in a negative number.
t is critical to evaluate both positive and negative solutions from the quadratic formula and consider the context of the problem to determine which solution is correct. In the examples, the negative solutions are often discarded due to real-world constraints.