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He has left the room without explaining/ explanation.
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They left the house in a frightening/ frightful mess.
I see it as follows:
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He has left the room without explanation.–OK He has left the room without explaining [not finished. You need a follow-up here:…explaining himself\how much he loves her\how he got there.]
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–Expected wording here is a ‘frightful mess’. (‘frightful’ used for emphasis, especially of something bad). ‘Frightening’ (= terrifying) would sound differently—you’d expect to find something really stressful in such a house: damaged gas pipes\ heating system out of order (in freezing temperatures)\ deformed walls etc.