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Simplifying w(9w + 2) = 7 Reorder the terms: w(2 + 9w) = 7 (2 * w + 9w * w) = 7 (2w + 9w2) = 7 Solving 2w + 9w2 = 7 Solving for variable 'w'. Reorder the terms: -7 + 2w + 9w2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + 2w + 9w2 = 0 Factor a trinomial. (-1 + -1w)(7 + -9w) = 0Subproblem 1
Set the factor '(-1 + -1w)' equal to zero and attempt to solve: Simplifying -1 + -1w = 0 Solving -1 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1w = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1w = 0 + 1 -1w = 0 + 1 Combine like terms: 0 + 1 = 1 -1w = 1 Divide each side by '-1'. w = -1 Simplifying w = -1Subproblem 2
Set the factor '(7 + -9w)' equal to zero and attempt to solve: Simplifying 7 + -9w = 0 Solving 7 + -9w = 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 + -9w = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -9w = 0 + -7 -9w = 0 + -7 Combine like terms: 0 + -7 = -7 -9w = -7 Divide each side by '-9'. w = 0.7777777778 Simplifying w = 0.7777777778Solution
w = {-1, 0.7777777778}
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