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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. (-7 + -1w)(11 + -2w) = 0Subproblem 1
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 = -7Subproblem 2
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 = 5.5Solution
w = {-7, 5.5}
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