To determine which of the given quadratic equations can be solved by grouping, we typically look for an expression that can be factored into two binomials. Grouping is a technique often used when the quadratic can be rearranged into two pairs that can be grouped together.
Let's analyze each equation one by one:
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\(x^2 - 4x - 8 = 0\):
- Factoring group: Not easily factorable with integers.
- Not suitable for grouping.
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\(x^2 + 8x - 22 = 0\):
- Factoring group: The quadratic can be rearranged, but does not lend itself to easy splitting.
- Not suitable for grouping.
-
\(x^2 - 12x + 18 = 0\):
- This can be factorable by finding factors of 18 that add up to -12.
- Factors are not integers.
- Not suitable for grouping.
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\(x^2 + 10x + 21 = 0\):
- This can be factored easily as \((x + 3)(x + 7) = 0\).
- Can be grouped into pairs leading to a solution.
- Suitable for grouping.
After examining all options, the quadratic equation that can be solved by grouping is \(x^2 + 10x + 21 = 0\).