grammar - "Apply" and the passive voice

Try writing your sentence this way:

The problem was resolved by applying the following method. (or the aforementioned method.)

Change your verb to one more amenable to passive voice. "Was resolved" works for passive mode, and apply changes to the gerund form: applying, which is also passive when used this way. You get problem as your subject, and apply in passive form, though not as the verb directly applied to the subject. This is an acceptable passive voice form, though it is wordy.