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Simplifying w(2w + 3) = 119 Reorder the terms: w(3 + 2w) = 119 (3 * w + 2w * w) = 119 (3w + 2w2) = 119 Solving 3w + 2w2 = 119 Solving for variable 'w'. Reorder the terms: -119 + 3w + 2w2 = 119 + -119 Combine like terms: 119 + -119 = 0 -119 + 3w + 2w2 = 0 Factor a trinomial. (-17 + -2w)(7 + -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 '(7 + -1w)' equal to zero and attempt to solve: Simplifying 7 + -1w = 0 Solving 7 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1w = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1w = 0 + -7 -1w = 0 + -7 Combine like terms: 0 + -7 = -7 -1w = -7 Divide each side by '-1'. w = 7 Simplifying w = 7Solution
w = {-8.5, 7}
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