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Usually the easiest way to solve this kind of problem is to find two numbers whose sum is equal to the coefficient of the middle term, and whose product is equal to the product of the coefficients of the first and last terms. So in this case, we would want a product of 40, and a sum of -13. The only numbers that meet that condition are -8 and -5, so we'll use those, breaking the middle term down into two separate terms:
2x2 - 13x + 20 = 0
∴ 2x2 - 8x - 5x + 20 = 0
Now you can take a common factor out of both the first two terms and the last two terms, and group the like terms together, resulting in the answer you seek:
∴ 2x(x - 4) - 5(x - 4) = 0
∴ (2x - 5)(x - 4) = 0
∴ x ∈ {2.5, 4}
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∙ 14y ago
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