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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 + -1w + -2w2 = 1w + -1w + 2w2 + -2w2 Combine like terms: 1w + -1w = 0 28 + -1w + -2w2 = 0 + 2w2 + -2w2 28 + -1w + -2w2 = 2w2 + -2w2 Combine like terms: 2w2 + -2w2 = 0 28 + -1w + -2w2 = 0 Factor a trinomial. (7 + -2w)(4 + w) = 0Subproblem 1
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 = 3.5Subproblem 2
Set the factor '(4 + w)' equal to zero and attempt to solve: Simplifying 4 + w = 0 Solving 4 + w = 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 + w = 0 + -4 Combine like terms: 4 + -4 = 0 0 + w = 0 + -4 w = 0 + -4 Combine like terms: 0 + -4 = -4 w = -4 Simplifying w = -4Solution
w = {3.5, -4}
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