To determine which of the given quadratic equations can be solved by grouping, we need to look for a quadratic equation that can be factored into two binomials where the middle term can be expressed as a sum of two terms.
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\(x^2 + 8x - 22 = 0\): This does not factor neatly into a product of binomials, and grouping would not be straightforward.
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\(x^2 - 12x + 18 = 0\): This also does not factor nicely using grouping.
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\(x^2 + 10x + 21 = 0\): This can be factored as \( (x + 3)(x + 7) = 0\), but there is no need for grouping here; it's simply factoring, but it does not utilize the grouping method.
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\(x^2 - 4x - 8 = 0\): Rewriting it as \( x^2 - 4x + 4 - 12 = 0 \), we get \( (x - 2)^2 - 12 = 0 \), which can be solved more easily by completing the square or factoring directly; however, it requires manipulation similar to grouping.
Of all the options, none of them straightforwardly fit the grouping method, but \(x^2 - 4x - 8 = 0\) may lead to a more complex problem that can involve grouping indirectly.
The best candidate is generally considered to be:
\(x^2 - 4x - 8 = 0\) since you can rearrange or manipulate it in a way that resembles grouping.