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Simplifying 77 = w(2w + 3) Reorder the terms: 77 = w(3 + 2w) 77 = (3 * w + 2w * w) 77 = (3w + 2w2) Solving 77 = 3w + 2w2 Solving for variable 'w'. Reorder the terms: 77 + -3w + -2w2 = 3w + -3w + 2w2 + -2w2 Combine like terms: 3w + -3w = 0 77 + -3w + -2w2 = 0 + 2w2 + -2w2 77 + -3w + -2w2 = 2w2 + -2w2 Combine like terms: 2w2 + -2w2 = 0 77 + -3w + -2w2 = 0 Factor a trinomial. (11 + -2w)(7 + w) = 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 + w)' equal to zero and attempt to solve: Simplifying 7 + w = 0 Solving 7 + w = 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 + w = 0 + -7 Combine like terms: 7 + -7 = 0 0 + w = 0 + -7 w = 0 + -7 Combine like terms: 0 + -7 = -7 w = -7 Simplifying w = -7Solution
w = {5.5, -7}
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