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Simplifying (9 + -1w)(4w + 2) = 0 Reorder the terms: (9 + -1w)(2 + 4w) = 0 Multiply (9 + -1w) * (2 + 4w) (9(2 + 4w) + -1w * (2 + 4w)) = 0 ((2 * 9 + 4w * 9) + -1w * (2 + 4w)) = 0 ((18 + 36w) + -1w * (2 + 4w)) = 0 (18 + 36w + (2 * -1w + 4w * -1w)) = 0 (18 + 36w + (-2w + -4w2)) = 0 Combine like terms: 36w + -2w = 34w (18 + 34w + -4w2) = 0 Solving 18 + 34w + -4w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2'. 2(9 + 17w + -2w2) = 0 Factor a trinomial. 2((9 + -1w)(1 + 2w)) = 0 Ignore the factor 2.Subproblem 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 '(1 + 2w)' equal to zero and attempt to solve: Simplifying 1 + 2w = 0 Solving 1 + 2w = 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 + 2w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2w = 0 + -1 2w = 0 + -1 Combine like terms: 0 + -1 = -1 2w = -1 Divide each side by '2'. w = -0.5 Simplifying w = -0.5Solution
w = {9, -0.5}
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