Sample question: "Creo que yo estoy a punto de encontrar la solución."
Is there a reason the "estoy" isn't subjunctive? If it were "espero que" instead of "creo que" would that matter?
You would need to say No creo que for the subsequent sentence to be in the subjunctive. This is because negative opinion phrases use the subjunctive. Other examples would be No pienso que, no estoy segura de que. If you just write pienso que or estoy segura de que it would take the indicative. Espero que however, always takes the subjunctive.
it is exactly as Marsha was saying and here is a lesson on this specific topic.
Have a look. Using the subjunctive with negative opinion phrases
I hope it is helpful.
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