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Simplifying (2w + -1) * w = 21 Reorder the terms: (-1 + 2w) * w = 21 Reorder the terms for easier multiplication: w(-1 + 2w) = 21 (-1 * w + 2w * w) = 21 (-1w + 2w2) = 21 Solving -1w + 2w2 = 21 Solving for variable 'w'. Reorder the terms: -21 + -1w + 2w2 = 21 + -21 Combine like terms: 21 + -21 = 0 -21 + -1w + 2w2 = 0 Factor a trinomial. (-3 + -1w)(7 + -2w) = 0Subproblem 1
Set the factor '(-3 + -1w)' equal to zero and attempt to solve: Simplifying -3 + -1w = 0 Solving -3 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1w = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1w = 0 + 3 -1w = 0 + 3 Combine like terms: 0 + 3 = 3 -1w = 3 Divide each side by '-1'. w = -3 Simplifying w = -3Subproblem 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 = {-3, 3.5}
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