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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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