Final answer:
Solving the complex equation for variable x requires using a quadratic formula after simplifying the equation by assuming x is negligibly small due to weak acid ionization, which is justified as the resulting value of x is much smaller than the initial concentration.
Step-by-step explanation:
The student's question involves solving for the variable x in a complex equation. To simplify the problem, one can assume that x is much smaller than other constants in the equation due to the small extent of ionization of weak acids. By omitting x in the denominator, we arrive at an equation that can be rearranged into a quadratic equation.
Since we are dealing with a quadratic equation of the form ax² + bx + c = 0, we can apply the quadratic formula to find the possible values for x. After plugging in the simplified values and solving, we compare the calculated x with the initial concentration to confirm the validity of our simplification. In this case, we find that the value of x is indeed much less than the initial concentration, which justifies our approximation.