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The phrase "was reached through" is correct and usable in written English.
It can be used to indicate the method or process by which something was achieved or obtained. Example: "The agreement was reached through extensive negotiations between the two parties."
Exact(60)
The long many-orielled battlemented house was reached through exquisite woods feathering down to the Derwent.
A compromise was reached through the "America Speaking Out" tour, which is set to begin Tuesday.
And the settlement was reached through court-recommended mediation, not through arbitration.
Tillotson said Armstrong's lies, as outlined in the agency's report, had changed the understanding that was reached through arbitration.
The husband, who like others in this article was reached through his lawyer, said the decision to invade his wife's privacy was not an easy one.
Plus ça change … but in the 18th century, alchemical delight was reached through symphonies rather than through anything more – well, chemical.
Mr. Chestnut, who was reached through the car research site Edmunds.com, said he first shopped for the Lexus RX330 before he learned about the hybrid version.
A settlement from 2005, which was reached through mediation, had capped publishers' liabilities at $18 million and released them from the possibility of further litigation.
This was reached through numerical experimentations.
The pressure was reached through use of a hydraulic jack (Figs. 2 and 3).
The improvement was reached through the updating of the cross-section library.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com