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Simplifying 14 = (2w + -3) * w Reorder the terms: 14 = (-3 + 2w) * w Reorder the terms for easier multiplication: 14 = w(-3 + 2w) 14 = (-3 * w + 2w * w) 14 = (-3w + 2w2) Solving 14 = -3w + 2w2 Solving for variable 'w'. Reorder the terms: 14 + 3w + -2w2 = -3w + 3w + 2w2 + -2w2 Combine like terms: -3w + 3w = 0 14 + 3w + -2w2 = 0 + 2w2 + -2w2 14 + 3w + -2w2 = 2w2 + -2w2 Combine like terms: 2w2 + -2w2 = 0 14 + 3w + -2w2 = 0 Factor a trinomial. (7 + -2w)(2 + 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 '(2 + w)' equal to zero and attempt to solve: Simplifying 2 + w = 0 Solving 2 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + w = 0 + -2 Combine like terms: 2 + -2 = 0 0 + w = 0 + -2 w = 0 + -2 Combine like terms: 0 + -2 = -2 w = -2 Simplifying w = -2Solution
w = {3.5, -2}
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