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Simplifying (7 + 2w) * w = 99 Reorder the terms for easier multiplication: w(7 + 2w) = 99 (7 * w + 2w * w) = 99 (7w + 2w2) = 99 Solving 7w + 2w2 = 99 Solving for variable 'w'. Reorder the terms: -99 + 7w + 2w2 = 99 + -99 Combine like terms: 99 + -99 = 0 -99 + 7w + 2w2 = 0 Factor a trinomial. (-9 + -1w)(11 + -2w) = 0Subproblem 1
Set the factor '(-9 + -1w)' equal to zero and attempt to solve: Simplifying -9 + -1w = 0 Solving -9 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1w = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1w = 0 + 9 -1w = 0 + 9 Combine like terms: 0 + 9 = 9 -1w = 9 Divide each side by '-1'. w = -9 Simplifying w = -9Subproblem 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 = {-9, 5.5}
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