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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 + -1w + -2w2 = 1w + -1w + 2w2 + -2w2 Combine like terms: 1w + -1w = 0 45 + -1w + -2w2 = 0 + 2w2 + -2w2 45 + -1w + -2w2 = 2w2 + -2w2 Combine like terms: 2w2 + -2w2 = 0 45 + -1w + -2w2 = 0 Factor a trinomial. (9 + -2w)(5 + w) = 0Subproblem 1
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 = 4.5Subproblem 2
Set the factor '(5 + w)' equal to zero and attempt to solve: Simplifying 5 + w = 0 Solving 5 + w = 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 + w = 0 + -5 Combine like terms: 5 + -5 = 0 0 + w = 0 + -5 w = 0 + -5 Combine like terms: 0 + -5 = -5 w = -5 Simplifying w = -5Solution
w = {4.5, -5}
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