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Simplifying 9(w2 + 1) = 9 + -1w Reorder the terms: 9(1 + w2) = 9 + -1w (1 * 9 + w2 * 9) = 9 + -1w (9 + 9w2) = 9 + -1w Add '-9' to each side of the equation. 9 + -9 + 9w2 = 9 + -9 + -1w Combine like terms: 9 + -9 = 0 0 + 9w2 = 9 + -9 + -1w 9w2 = 9 + -9 + -1w Combine like terms: 9 + -9 = 0 9w2 = 0 + -1w 9w2 = -1w Solving 9w2 = -1w Solving for variable 'w'. Reorder the terms: w + 9w2 = -1w + w Combine like terms: -1w + w = 0 w + 9w2 = 0 Factor out the Greatest Common Factor (GCF), 'w'. w(1 + 9w) = 0Subproblem 1
Set the factor 'w' equal to zero and attempt to solve: Simplifying w = 0 Solving w = 0 Move all terms containing w to the left, all other terms to the right. Simplifying w = 0Subproblem 2
Set the factor '(1 + 9w)' equal to zero and attempt to solve: Simplifying 1 + 9w = 0 Solving 1 + 9w = 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 + 9w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 9w = 0 + -1 9w = 0 + -1 Combine like terms: 0 + -1 = -1 9w = -1 Divide each side by '9'. w = -0.1111111111 Simplifying w = -0.1111111111Solution
w = {0, -0.1111111111}
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