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Simplifying -12w + -5 = 4w2 Reorder the terms: -5 + -12w = 4w2 Solving -5 + -12w = 4w2 Solving for variable 'w'. Combine like terms: 4w2 + -4w2 = 0 -5 + -12w + -4w2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(5 + 12w + 4w2) = 0 Factor a trinomial. -1((5 + 2w)(1 + 2w)) = 0 Ignore the factor -1.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 + 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 = {-2.5, -0.5}
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