Final answer:
The mistake in the equation x - 78 = -42 involves incorrect use of inverse operations; the correct solution is x = 36. When solving quadratic equations like 0.000484 - 0.00088x = x², the negative value (-0.0024) is discarded as concentrations cannot be negative, thus x = 0.00139 is the accurate value. An answer of 88 °C would be incorrect for such a small coefficient value in the context of the equilibrium constant.
Step-by-step explanation:
The solution to the equation provided is inaccurate because it displays a misunderstanding of the correct steps to isolate the variable x. The original equation includes x - 78 = -42. To solve for x, one should add 78 to both sides of the equation, giving x = -42 + 78. Accordingly, x would equal 36, not -36 as incorrectly stated. It is important to maintain the proper order of operations and correctly apply inverse operations to solve equations.
When working with a quadratic equation such as 0.000484 - 0.00088x = x², the quadratic formula should be applied correctly. The student's usage of the quadratic equation to find the values of x yielded x = -0.0024 and x = 0.00139. Since negative concentrations do not exist in real-life scenarios, the value of x equaling -0.0024 is dismissed, and the actual solution is x = 0.00139.
Giving an answer of 88 °C is clearly incorrect if the context implies that it should be within the magnitude of the coefficients involved in the quadratic equation. In the situation of equilibrium constant calculations, assuming x to be much smaller than the initial concentrations, such as (0.78 - x) ≈ 0.78 and (0.21 - x) ≈ 0.21 simplifies the equation and makes solving for x more manageable. An answer as high as 88 °C would not be consistent with typical results involving such small coefficient values.