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The phrase "achieved an equal" is correct and usable in written English.
It can be used in contexts where one is discussing reaching a level of equality or parity in a certain aspect, such as performance, status, or achievement.
Example: "After years of hard work, she finally achieved an equal in her field, earning the same recognition as her male counterparts."
Alternatives: "reached parity" or "attained equality".
Exact(7)
But the company also achieved an equal cut in the ships' emissions of greenhouse gases.
But with seeming unanimity, Poles say they view their country's entry as proof that they have achieved an equal footing with their partners to the west.
The language verification system achieved an equal error rate for European Portuguese of 2.5%.
From Table 5, we achieved an equal recognition rate compared to the system of Ma et al. on the CASIA-I dataset.
We carried out an Affymetrix microarray analysis of 4 pairs of null vs. wild type day 8.5 siblings that had achieved an equal level of development as judged during dissection.
With the exception of escitalopram, the favoured antidepressants achieved an equal or higher median rating in round two compared to round one, whereas the antidepressants considered less appropriate, achieved an equal or lower median rating in the second round.
Similar(53)
But over the longer term, he predicted EADS would achieve an equal balance between the two divisions.
Overprotection is another barrier preventing disabled girls in India achieving an equal level of education, which in turn keeps them in menial low paying jobs.
She is chairwoman of the Institute of Practitioners of Advertising's Creative Forum and is doing her damnedest to achieve an equal balance between men and women in her own agency's creative teams.
Though often compared to Giorgio Morandi's pared-down still lifes, Mr. Pesce's paintings are more forthrightly geometric and grander in scale; space, paint and object achieve an equal density yet remained distinct.
The story is simply this: the persistence of women in their struggle to achieve an equal chance to determine their own destinies and to be acknowledged for their full contribution to the survival and thriving of the human race as a whole.
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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