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Simplifying 45 = w(2w + -1) Reorder the terms: 45 = w(-1 + 2w) 45 = (-1 * w + 2w * w) 45 = (-1w + 2w2) Solving 45 = -1w + 2w2 Solving for variable 'w'. Reorder the terms: 45 + w + -2w2 = -1w + w + 2w2 + -2w2 Combine like terms: -1w + w = 0 45 + w + -2w2 = 0 + 2w2 + -2w2 45 + w + -2w2 = 2w2 + -2w2 Combine like terms: 2w2 + -2w2 = 0 45 + w + -2w2 = 0 Factor a trinomial. (5 + -1w)(9 + 2w) = 0Subproblem 1
Set the factor '(5 + -1w)' equal to zero and attempt to solve: Simplifying 5 + -1w = 0 Solving 5 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1w = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1w = 0 + -5 -1w = 0 + -5 Combine like terms: 0 + -5 = -5 -1w = -5 Divide each side by '-1'. w = 5 Simplifying w = 5Subproblem 2
Set the factor '(9 + 2w)' equal to zero and attempt to solve: Simplifying 9 + 2w = 0 Solving 9 + 2w = 0 Move all terms containing w to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 2w = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 2w = 0 + -9 2w = 0 + -9 Combine like terms: 0 + -9 = -9 2w = -9 Divide each side by '2'. w = -4.5 Simplifying w = -4.5Solution
w = {5, -4.5}
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