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Simplifying 4w2 + 4w + 10w + 10 = 0 Reorder the terms: 10 + 4w + 10w + 4w2 = 0 Combine like terms: 4w + 10w = 14w 10 + 14w + 4w2 = 0 Solving 10 + 14w + 4w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2'. 2(5 + 7w + 2w2) = 0 Factor a trinomial. 2((5 + 2w)(1 + w)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + 2w)' equal to zero and attempt to solve: Simplifying 5 + 2w = 0 Solving 5 + 2w = 0 Move all terms containing w to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 2w = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2w = 0 + -5 2w = 0 + -5 Combine like terms: 0 + -5 = -5 2w = -5 Divide each side by '2'. w = -2.5 Simplifying w = -2.5Subproblem 2
Set the factor '(1 + w)' equal to zero and attempt to solve: Simplifying 1 + w = 0 Solving 1 + w = 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 + w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + w = 0 + -1 w = 0 + -1 Combine like terms: 0 + -1 = -1 w = -1 Simplifying w = -1Solution
w = {-2.5, -1}
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