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Simplifying (2w + -3) * w = 14 Reorder the terms: (-3 + 2w) * w = 14 Reorder the terms for easier multiplication: w(-3 + 2w) = 14 (-3 * w + 2w * w) = 14 (-3w + 2w2) = 14 Solving -3w + 2w2 = 14 Solving for variable 'w'. Reorder the terms: -14 + -3w + 2w2 = 14 + -14 Combine like terms: 14 + -14 = 0 -14 + -3w + 2w2 = 0 Factor a trinomial. (-2 + -1w)(7 + -2w) = 0Subproblem 1
Set the factor '(-2 + -1w)' equal to zero and attempt to solve: Simplifying -2 + -1w = 0 Solving -2 + -1w = 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 + -1w = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1w = 0 + 2 -1w = 0 + 2 Combine like terms: 0 + 2 = 2 -1w = 2 Divide each side by '-1'. w = -2 Simplifying w = -2Subproblem 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 = {-2, 3.5}
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