Final answer:
To find the value of x, solve the quadratic equation using the quadratic formula. Discard any non-physical solutions, such as negative values in contexts where they do not make sense. Confirm assumptions to decide if a simpler method can be used.
Step-by-step explanation:
To find the value of x, we need to solve the given quadratic equation. Considering the equation has the form x² + (constant)x + (constant) = 0, we can utilize the quadratic formula to find the roots of the equation. However, before using the quadratic formula, we should verify if the provided equation can be simplified or if there's a more straightforward method to solve it, such as factoring.
For example, if the left side of the equation appears to be a perfect square, it can simplify our work. If a solution we find is negative and this does not make sense in the context (such as negative concentrations in chemistry, where x typically represents concentration), this solution can be discarded. In physical science problems, negative amounts are often non-physical and thus disregarded, leaving us with the positive value as the viable solution.
Once we obtain the possible values of x, we confirm whether our assumptions were correct. For instance, if the assumption that x is less than 5% of the initial concentration (a common assumption in equilibrium problems) is incorrect, we must use the more accurate method, such as the quadratic formula, to find the correct value of x.