To determine which quadratic equation is not solvable by grouping, we need to analyze each equation to see if its coefficients allow for factoring by grouping.
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\(2x^2 - 2x - 10 = 0\): This can be factored as \(2(x^2 - x - 5) = 0\), leading to a manageable quadratic that can be solved by factoring or using the quadratic formula.
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\(2x^2 + 14x + 12 = 0\): This can be factored as \(2(x^2 + 7x + 6) = 0\) which can be factored further as \(2(x + 6)(x + 1) = 0\).
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\(x^2 - 2x + 1 = 0\): This can be factored as \((x - 1)(x - 1) = 0\) or \((x - 1)^2 = 0\).
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\(x^2 - 12x + 35 = 0\): This can be factored as \((x - 5)(x - 7) = 0\).
All the given quadratic equations can be factored easily using standard methods, including grouping. However, the first option \(2x^2 - 2x - 10 = 0\) would not typically lend itself to the grouping method because it is more straightforward to factor out the common factor first (\(2\)) and then solve the resulting quadratic. Grouping is generally best applied to quadratics that do not have a straightforward representation.
Therefore, while all equations could technically be solved by standard methods, the one that is "not solvable by grouping" would be the first option due to its nature. But note that groupings are contingent on specific arrangements of terms. In summary, the most likely candidate here is:
\(2x^2 - 2x - 10 = 0\).