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Simplifying 2w(4w + 10) = -8 Reorder the terms: 2w(10 + 4w) = -8 (10 * 2w + 4w * 2w) = -8 (20w + 8w2) = -8 Solving 20w + 8w2 = -8 Solving for variable 'w'. Reorder the terms: 8 + 20w + 8w2 = -8 + 8 Combine like terms: -8 + 8 = 0 8 + 20w + 8w2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(2 + 5w + 2w2) = 0 Factor a trinomial. 4((2 + w)(1 + 2w)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(2 + w)' equal to zero and attempt to solve: Simplifying 2 + w = 0 Solving 2 + w = 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 + w = 0 + -2 Combine like terms: 2 + -2 = 0 0 + w = 0 + -2 w = 0 + -2 Combine like terms: 0 + -2 = -2 w = -2 Simplifying w = -2Subproblem 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 = {-2, -0.5}
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