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Simplifying (2w + -9) * w = 110 Reorder the terms: (-9 + 2w) * w = 110 Reorder the terms for easier multiplication: w(-9 + 2w) = 110 (-9 * w + 2w * w) = 110 (-9w + 2w2) = 110 Solving -9w + 2w2 = 110 Solving for variable 'w'. Reorder the terms: -110 + -9w + 2w2 = 110 + -110 Combine like terms: 110 + -110 = 0 -110 + -9w + 2w2 = 0 Factor a trinomial. (-11 + -2w)(10 + -1w) = 0Subproblem 1
Set the factor '(-11 + -2w)' equal to zero and attempt to solve: Simplifying -11 + -2w = 0 Solving -11 + -2w = 0 Move all terms containing w to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + -2w = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -2w = 0 + 11 -2w = 0 + 11 Combine like terms: 0 + 11 = 11 -2w = 11 Divide each side by '-2'. w = -5.5 Simplifying w = -5.5Subproblem 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 = {-5.5, 10}
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