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Simplifying w(2w + -1) = 91 Reorder the terms: w(-1 + 2w) = 91 (-1 * w + 2w * w) = 91 (-1w + 2w2) = 91 Solving -1w + 2w2 = 91 Solving for variable 'w'. Reorder the terms: -91 + -1w + 2w2 = 91 + -91 Combine like terms: 91 + -91 = 0 -91 + -1w + 2w2 = 0 Factor a trinomial. (-13 + -2w)(7 + -1w) = 0Subproblem 1
Set the factor '(-13 + -2w)' equal to zero and attempt to solve: Simplifying -13 + -2w = 0 Solving -13 + -2w = 0 Move all terms containing w to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + -2w = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -2w = 0 + 13 -2w = 0 + 13 Combine like terms: 0 + 13 = 13 -2w = 13 Divide each side by '-2'. w = -6.5 Simplifying w = -6.5Subproblem 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 = {-6.5, 7}
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