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The phrase "a task that would" is correct and usable in written English.
It can be used when describing a task that has a certain potential or outcome associated with it.
Example: "Completing a task that would improve team efficiency is essential for our success."
Alternatives: "a task that might" or "a task that could".
Exact(56)
First, we decided upon a task that would accurately denote Hebbian learning.
Overcoming that legacy is a task that would tax any successor government.
I decided to set up a task that would be challenging enough even for a native speaker to undertake.
Lawyers said defining which groups were political ones was a task that would not pass legal scrutiny.
I won't be able to provide personalized restaurant recommendations, a task that would be unsustainably time-consuming.
What dazzled him was the city itself, the center of a pan-European culture, which he aspired to join — a task that would not be easy.
Part of the Sound Research Laboratories' brief was to develop new instruments to measure low-frequency sound, a task that would, sufferers argue, demand far larger funds.
Similar(4)
The BBC has used the centre to complete a music task that would have taken over a year in an astonishing twelve hours.
Technology today can do in five minutes a decoding task that would have taken a year to complete a decade ago, Lander said.
Quantum supremacy is the term that describes a quantum computer's ability to solve a computational task that would be prohibitively difficult for any classical algorithm.
Establishing an effective and inclusive security system for the Euro-Atlantic region is an important task that would have a profound impact in removing sources of tension and suspicion in our relations.
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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