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Simplifying 28 = w(2w + -1) Reorder the terms: 28 = w(-1 + 2w) 28 = (-1 * w + 2w * w) 28 = (-1w + 2w2) Solving 28 = -1w + 2w2 Solving for variable 'w'. Reorder the terms: 28 + w + -2w2 = -1w + w + 2w2 + -2w2 Combine like terms: -1w + w = 0 28 + w + -2w2 = 0 + 2w2 + -2w2 28 + w + -2w2 = 2w2 + -2w2 Combine like terms: 2w2 + -2w2 = 0 28 + w + -2w2 = 0 Factor a trinomial. (4 + -1w)(7 + 2w) = 0Subproblem 1
Set the factor '(4 + -1w)' equal to zero and attempt to solve: Simplifying 4 + -1w = 0 Solving 4 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1w = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1w = 0 + -4 -1w = 0 + -4 Combine like terms: 0 + -4 = -4 -1w = -4 Divide each side by '-1'. w = 4 Simplifying w = 4Subproblem 2
Set the factor '(7 + 2w)' equal to zero and attempt to solve: Simplifying 7 + 2w = 0 Solving 7 + 2w = 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 + 2w = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 2w = 0 + -7 2w = 0 + -7 Combine like terms: 0 + -7 = -7 2w = -7 Divide each side by '2'. w = -3.5 Simplifying w = -3.5Solution
w = {4, -3.5}
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