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You would test each value with the equilibrium expression that was found using the ICE table to see if the value is reasonable. Usually one of the values found using the quadratic equation will cause one of the concentrations to be negative, which is not possible.
If you use the quadratic formula and get two positive answers, you would choose the answer where if you subtract it from any of the initial conditions given it would be result in a reasonable and nonnegative concentration or pressure.
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