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Simplifying (2w + -3) * w = 170 Reorder the terms: (-3 + 2w) * w = 170 Reorder the terms for easier multiplication: w(-3 + 2w) = 170 (-3 * w + 2w * w) = 170 (-3w + 2w2) = 170 Solving -3w + 2w2 = 170 Solving for variable 'w'. Reorder the terms: -170 + -3w + 2w2 = 170 + -170 Combine like terms: 170 + -170 = 0 -170 + -3w + 2w2 = 0 Factor a trinomial. (-17 + -2w)(10 + -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 '(10 + -1w)' equal to zero and attempt to solve: Simplifying 10 + -1w = 0 Solving 10 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1w = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1w = 0 + -10 -1w = 0 + -10 Combine like terms: 0 + -10 = -10 -1w = -10 Divide each side by '-1'. w = 10 Simplifying w = 10Solution
w = {-8.5, 10}
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