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Simplifying 2w2 + 12w + 19 + -1w2 + -4w + -4 = 0 Reorder the terms: 19 + -4 + 12w + -4w + 2w2 + -1w2 = 0 Combine like terms: 19 + -4 = 15 15 + 12w + -4w + 2w2 + -1w2 = 0 Combine like terms: 12w + -4w = 8w 15 + 8w + 2w2 + -1w2 = 0 Combine like terms: 2w2 + -1w2 = 1w2 15 + 8w + 1w2 = 0 Solving 15 + 8w + 1w2 = 0 Solving for variable 'w'. Factor a trinomial. (5 + w)(3 + w) = 0Subproblem 1
Set the factor '(5 + w)' equal to zero and attempt to solve: Simplifying 5 + w = 0 Solving 5 + w = 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 + w = 0 + -5 Combine like terms: 5 + -5 = 0 0 + w = 0 + -5 w = 0 + -5 Combine like terms: 0 + -5 = -5 w = -5 Simplifying w = -5Subproblem 2
Set the factor '(3 + w)' equal to zero and attempt to solve: Simplifying 3 + w = 0 Solving 3 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + w = 0 + -3 Combine like terms: 3 + -3 = 0 0 + w = 0 + -3 w = 0 + -3 Combine like terms: 0 + -3 = -3 w = -3 Simplifying w = -3Solution
w = {-5, -3}
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