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Simplifying 0 = 4w2 + -11w + -20 Reorder the terms: 0 = -20 + -11w + 4w2 Solving 0 = -20 + -11w + 4w2 Solving for variable 'w'. Combine like terms: 0 + 20 = 20 20 + 11w + -4w2 = -20 + -11w + 4w2 + 20 + 11w + -4w2 Reorder the terms: 20 + 11w + -4w2 = -20 + 20 + -11w + 11w + 4w2 + -4w2 Combine like terms: -20 + 20 = 0 20 + 11w + -4w2 = 0 + -11w + 11w + 4w2 + -4w2 20 + 11w + -4w2 = -11w + 11w + 4w2 + -4w2 Combine like terms: -11w + 11w = 0 20 + 11w + -4w2 = 0 + 4w2 + -4w2 20 + 11w + -4w2 = 4w2 + -4w2 Combine like terms: 4w2 + -4w2 = 0 20 + 11w + -4w2 = 0 Factor a trinomial. (4 + -1w)(5 + 4w) = 0Subproblem 1
Set the factor '(4 + -1w)' equal to zero and attempt to solve: Simplifying 4 + -1w = 0 Solving 4 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1w = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1w = 0 + -4 -1w = 0 + -4 Combine like terms: 0 + -4 = -4 -1w = -4 Divide each side by '-1'. w = 4 Simplifying w = 4Subproblem 2
Set the factor '(5 + 4w)' equal to zero and attempt to solve: Simplifying 5 + 4w = 0 Solving 5 + 4w = 0 Move all terms containing w to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 4w = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 4w = 0 + -5 4w = 0 + -5 Combine like terms: 0 + -5 = -5 4w = -5 Divide each side by '4'. w = -1.25 Simplifying w = -1.25Solution
w = {4, -1.25}
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