To determine which of the given quadratic equations can be solved by grouping, we need to look for an equation where we can split the middle term into two terms that can be grouped and factored.
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x² + 8x - 22 = 0: The middle term (8) does not factor nicely with the other terms for grouping.
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x² - 12x + 18 = 0: We look for two numbers that multiply to 18 (the constant term) and add to -12 (the middle term). The numbers -6 and -6 would work for adding but not for grouping since they do not have distinct factors.
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x² - 4x - 8 = 0: Similar situation; we need two factors of -8 that add to -4. The factors 2 and -4 could work, but again wouldn't allow for effective grouping.
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x² + 10x + 21 = 0: Here, we can factor this as (x + 3)(x + 7) = 0, which is a straightforward factoring instead of grouping.
Based on factorability, none of these equations truly lend themselves to grouping very well. However, if we must pick one, the equation x² + 10x + 21 = 0 would be the best choice for straightforward factoring, though it technically doesn’t require grouping to be solved.
In the context of grouping, typically you look for quadratics that can create two binomials around a shared term—which is tricky with the options given.
That said, if you are particularly focusing on which quadratic can be rearranged to allow for grouping, it would be best to specifically check for common factors or favorable splits in the middle term, none of which fully satisfy that in this list.
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