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Simplifying (2w + -3)(w) = 77 Reorder the terms: (-3 + 2w)(w) = 77 Reorder the terms for easier multiplication: w(-3 + 2w) = 77 (-3 * w + 2w * w) = 77 (-3w + 2w2) = 77 Solving -3w + 2w2 = 77 Solving for variable 'w'. Reorder the terms: -77 + -3w + 2w2 = 77 + -77 Combine like terms: 77 + -77 = 0 -77 + -3w + 2w2 = 0 Factor a trinomial. (-11 + -2w)(7 + -1w) = 0Subproblem 1
Set the factor '(-11 + -2w)' equal to zero and attempt to solve: Simplifying -11 + -2w = 0 Solving -11 + -2w = 0 Move all terms containing w to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + -2w = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -2w = 0 + 11 -2w = 0 + 11 Combine like terms: 0 + 11 = 11 -2w = 11 Divide each side by '-2'. w = -5.5 Simplifying w = -5.5Subproblem 2
Set the factor '(7 + -1w)' equal to zero and attempt to solve: Simplifying 7 + -1w = 0 Solving 7 + -1w = 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 + -1w = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1w = 0 + -7 -1w = 0 + -7 Combine like terms: 0 + -7 = -7 -1w = -7 Divide each side by '-1'. w = 7 Simplifying w = 7Solution
w = {-5.5, 7}
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