To determine which of the given quadratic equations can be solved by grouping, we need to find one that can be factored into two binomials, where the middle term can be split into two terms that can be grouped together.
Let's analyze each equation:
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\(x^2 + 8x - 22 = 0\): This doesn't factor nicely, and grouping would not be straightforward.
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\(x^2 - 4x - 8 = 0\): This also does not factor nicely into integers, and grouping does not apply well here.
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\(x^2 + 10x + 21 = 0\): This equation factors nicely since \(10\) can be split into \(3\) and \(7\) (i.e., \((x + 3)(x + 7) = 0\)). It can be solved by factoring directly, but not necessarily by grouping.
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\(x^2 - 12x + 18 = 0\): This does not factor easily into integers; no straightforward grouping.
Among the choices provided, none are easily solved by grouping. However, if we were to apply the grouping technique, it is most often applicable when terms can be rearranged into pairs that share common factors, which is not the case here.
In conclusion, if you are specifically asked for the one that has the best potential for grouping, the quadratic \(x^2 + 10x + 21 = 0\) is the closest, but it is more suitable for direct factoring than for grouping.
Thus, answers like "none" or "the third one" might depend on how strictly one interprets "solved by grouping." If the option is that grouping must be inherently part of the solving method, None of the equations is solved by that.