[robstamos]

Consider the following balanced chemical equation:

CH4(g) + H2O(g)  ⟷  CO(g)  + 3 H2(g)

A reaction mixture initially contains 3.1 M CH4 and 1.90 M H2O.  Determine the equilibrium concentration of CH4 if Kc for the reaction at this temperature is 2.10 x 10-5.

I know how to start this problem, just having trouble finishing it.

When solving after using the quadratic formula I get 3.1 = 27x^4 and 1.9 = 27x^4; however, after solving for x neither of these are correct. The final right answer is x = 0.0463 and the equilibrium concentration of CH4 is 3.0537. Does anybody have an idea of where I'm going wrong here?

[AWK]

Solving quartic equation I got 0.0458 (sqrt(17)/90).
Your approximation correctly set gave 0.0463

https://www.symbolab.com/solver/polynomial-equation-calculator/%5Cfrac%7B27x%5E%7B4%7D%7D%7B%5Cleft(3.1-x%5Cright)%5Ccdot%5Cleft(1.9-x%5Cright)%7D%3D0.000021