To determine which quadratic equations can be solved by grouping, we need to look for equations that can be expressed in a way that allows us to factor them by grouping.
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For the equation \(x^2 - 12x + 18 = 0\):
- The factors of 18 that add up to -12 do not exist. (Factors: -2 and -9 do not work). Not suitable for grouping.
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For the equation \(x^2 + 8x - 22 = 0\):
- The factors of -22 that add up to 8 do not exist. Not suitable for grouping.
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For the equation \(x^2 + 10x + 21 = 0\):
- This can be factored as \((x + 3)(x + 7) = 0\), which is not a case of grouping. However, it is solvable by factoring.
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For the equation \(x^2 - 4x - 8 = 0\):
- We can rewrite it as \(x^2 - 4x - 8 = x^2 - 4x + 4 - 12 = (x - 2)^2 - 12\), but it's more straightforward to use factoring or the quadratic formula.
Conclusion: None of these equations can be solved by grouping in the traditional sense. However, if you're looking for a classic grouping style, options 1 and 2 do not fit, and the other two can be solved by factoring, but again not quite using the grouping method.
If we strictly consider grouping, none fully adhere, but equations that factor easily are preferable for basic methods.
Thus, to directly answer your query: none can be specifically solved by grouping as presented, as this method typically requires a clear setup of four terms to group.
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