The phrase 'a satisfactory reason' is correct and usable in written English.
You can use it when you are explaining why something has happened or why something should be accepted. For example: "The manager accepted my request for a flexible working schedule, with a satisfactory reason being that I am the primary caretaker for my ill mother."
Any person who cannot give a satisfactory reason for his staying in that region will be compulsorily recruited.
The Legal Aid Board have still to give me a satisfactory reason as to why this is the case," said Mr Santoni.
Dr. Bausch, the C.D.C. medical epidemiologist who joined in these chats nearly every night for two months, said no one could give Dr. Matthew a satisfactory reason why the nurses were getting infected.
The tavern may have been a contributing reason for the passage of a law that mandated no alcoholic drinks be served after 9 p.m. under penalty of a fine, unless a satisfactory reason was given to the constable or magistrate.
He even concocts the ruse of the Trojan horse (filled with Greek soldiers), though he adds that he could "never come up with a fully satisfactory reason why the Trojans would blithely drag a suspicious 50-foot-tall wooden statue into their city".
The only annoying thing about it is the ending, which, while offering a perfectly satisfactory reason for all of this Grecian theatricality, does seem to be trying very hard to herald a series two.
This, in my view, is a much more satisfactory reason for her newfound power over the ruby slippers than the sentimental reasons offered by the ineffably loopy Good Witch Glinda, and then by Dorothy herself, in a cloying ending that seems to me fundamentally untrue to the film's anarchic spirit.
No satisfactory reason given as to why… Talk story.
No satisfactory reason given as to why preview was held in this manner.
Knowledge requires reasons, and God can have no satisfactory reason for his belief, if by "satisfactory" we understand what the infallible omniscience usually attributed to him would require — namely, a reason that guarantees correctness.
No satisfactory reason has been given for why they are needed.
