Bot GPT 4-o mini To determine which of the quadratic equations is not solvable by grouping, we can analyze each equation to see if it can be factored using the method of grouping.
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\(x^2 - 12x + 35 = 0\): This can be factored as \((x - 5)(x - 7) = 0\).
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\(x^2 - 2x + 1 = 0\): This can be factored as \((x - 1)(x - 1) = 0\). This is also a perfect square.
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\(2x^2 + 14x + 12 = 0\): To factor this, we can first factor out a 2: \(2(x^2 + 7x + 6) = 0\), which can then be factored as \(2(x + 6)(x + 1) = 0\).
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\(2x^2 - 2x - 10 = 0\): We can factor out a 2 first: \(2(x^2 - x - 5) = 0\). The quadratic \(x^2 - x - 5\) does not factor neatly using integers, and the standard method of grouping doesn't apply here directly.
From this analysis, the fourth equation \(2x^2 - 2x - 10 = 0\) is not solvable by grouping because it does not factor nicely with integer values.
Therefore, the answer is: \(2x^2 - 2x - 10 = 0\).
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