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Simplifying 10w3 + 9w2 + 2w = 0 Reorder the terms: 2w + 9w2 + 10w3 = 0 Solving 2w + 9w2 + 10w3 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), 'w'. w(2 + 9w + 10w2) = 0 Factor a trinomial. w((1 + 2w)(2 + 5w)) = 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 + 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 = -0.5Subproblem 3
Set the factor '(2 + 5w)' equal to zero and attempt to solve: Simplifying 2 + 5w = 0 Solving 2 + 5w = 0 Move all terms containing w to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 5w = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 5w = 0 + -2 5w = 0 + -2 Combine like terms: 0 + -2 = -2 5w = -2 Divide each side by '5'. w = -0.4 Simplifying w = -0.4Solution
w = {0, -0.5, -0.4}
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