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Simplifying (2w + -7)(w) = 204 Reorder the terms: (-7 + 2w)(w) = 204 Reorder the terms for easier multiplication: w(-7 + 2w) = 204 (-7 * w + 2w * w) = 204 (-7w + 2w2) = 204 Solving -7w + 2w2 = 204 Solving for variable 'w'. Reorder the terms: -204 + -7w + 2w2 = 204 + -204 Combine like terms: 204 + -204 = 0 -204 + -7w + 2w2 = 0 Factor a trinomial. (-17 + -2w)(12 + -1w) = 0Subproblem 1
Set the factor '(-17 + -2w)' equal to zero and attempt to solve: Simplifying -17 + -2w = 0 Solving -17 + -2w = 0 Move all terms containing w to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + -2w = 0 + 17 Combine like terms: -17 + 17 = 0 0 + -2w = 0 + 17 -2w = 0 + 17 Combine like terms: 0 + 17 = 17 -2w = 17 Divide each side by '-2'. w = -8.5 Simplifying w = -8.5Subproblem 2
Set the factor '(12 + -1w)' equal to zero and attempt to solve: Simplifying 12 + -1w = 0 Solving 12 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1w = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1w = 0 + -12 -1w = 0 + -12 Combine like terms: 0 + -12 = -12 -1w = -12 Divide each side by '-1'. w = 12 Simplifying w = 12Solution
w = {-8.5, 12}
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