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Simplifying 0 = -20w2 + -55w + -30 Reorder the terms: 0 = -30 + -55w + -20w2 Solving 0 = -30 + -55w + -20w2 Solving for variable 'w'. Combine like terms: 0 + 30 = 30 30 + 55w + 20w2 = -30 + -55w + -20w2 + 30 + 55w + 20w2 Reorder the terms: 30 + 55w + 20w2 = -30 + 30 + -55w + 55w + -20w2 + 20w2 Combine like terms: -30 + 30 = 0 30 + 55w + 20w2 = 0 + -55w + 55w + -20w2 + 20w2 30 + 55w + 20w2 = -55w + 55w + -20w2 + 20w2 Combine like terms: -55w + 55w = 0 30 + 55w + 20w2 = 0 + -20w2 + 20w2 30 + 55w + 20w2 = -20w2 + 20w2 Combine like terms: -20w2 + 20w2 = 0 30 + 55w + 20w2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(6 + 11w + 4w2) = 0 Factor a trinomial. 5((2 + w)(3 + 4w)) = 0 Ignore the factor 5.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 '(3 + 4w)' equal to zero and attempt to solve: Simplifying 3 + 4w = 0 Solving 3 + 4w = 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 + 4w = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4w = 0 + -3 4w = 0 + -3 Combine like terms: 0 + -3 = -3 4w = -3 Divide each side by '4'. w = -0.75 Simplifying w = -0.75Solution
w = {-2, -0.75}
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