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"successfully achieve" is a correct and usable phrase in written English.
It can be used to describe the act of achieving or accomplishing something in a successful manner. Here is an example: After months of hard work and dedication, she was able to successfully achieve her goal of running a marathon.
Exact(60)
An economy of means makes you ever more resourceful and realistic about what an artist can successfully achieve in their exhibition or project.
Notwithstanding her membership of the Cambridge Nines - granted only to those who successfully achieve a third in every year of study - Carol's ability to tussle effortlessly with the most mind-bending number puzzles never ceased to amaze.
The smart city is no different – to successfully achieve it's smart city vision, a city and its providers must successfully navigate the political realities in a city and simultaneously avoid its pitfalls.
According to statistics from Statistic Brain, only 8 per cent of the US population manages to successfully achieve their New Year's resolution - if it were easy, you would have already done it.
In order to define and improve upon the early enthusiasm I felt for arts and crafts as a child, I studied hard to successfully achieve a BA in Graphic Design".
Consequently, we could successfully achieve the objectives established by the organization.
To successfully achieve such an allocation, several studies have considered the dynamic spectrum access (DSA) issues.
Thus, we can successfully achieve distinguishable X-ray attenuation of funguses.
Therefore, we successfully achieve the trade-off between security and performance.
Figure 7b presents that all the regions successfully achieve both the per-location fairness and service differentiation at each period.
Naidoo said that Ibrahim's genius was to successfully achieve an economy of scale in 15 African nations at the same time, while maintaining his integrity.
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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