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Simplifying (2w + 1) * w = 66 Reorder the terms: (1 + 2w) * w = 66 Reorder the terms for easier multiplication: w(1 + 2w) = 66 (1 * w + 2w * w) = 66 (1w + 2w2) = 66 Solving 1w + 2w2 = 66 Solving for variable 'w'. Reorder the terms: -66 + 1w + 2w2 = 66 + -66 Combine like terms: 66 + -66 = 0 -66 + 1w + 2w2 = 0 Factor a trinomial. (-6 + -1w)(11 + -2w) = 0Subproblem 1
Set the factor '(-6 + -1w)' equal to zero and attempt to solve: Simplifying -6 + -1w = 0 Solving -6 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1w = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1w = 0 + 6 -1w = 0 + 6 Combine like terms: 0 + 6 = 6 -1w = 6 Divide each side by '-1'. w = -6 Simplifying w = -6Subproblem 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 = {-6, 5.5}
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