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Simplifying 3w3 + -33w2 + -90w = 0 Reorder the terms: -90w + -33w2 + 3w3 = 0 Solving -90w + -33w2 + 3w3 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '3w'. 3w(-30 + -11w + w2) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'w' equal to zero and attempt to solve: Simplifying w = 0 Solving w = 0 Move all terms containing w to the left, all other terms to the right. Simplifying w = 0Subproblem 2
Set the factor '(-30 + -11w + w2)' equal to zero and attempt to solve: Simplifying -30 + -11w + w2 = 0 Solving -30 + -11w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '30' to each side of the equation. -30 + -11w + 30 + w2 = 0 + 30 Reorder the terms: -30 + 30 + -11w + w2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + -11w + w2 = 0 + 30 -11w + w2 = 0 + 30 Combine like terms: 0 + 30 = 30 -11w + w2 = 30 The w term is -11w. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11w + 30.25 + w2 = 30 + 30.25 Reorder the terms: 30.25 + -11w + w2 = 30 + 30.25 Combine like terms: 30 + 30.25 = 60.25 30.25 + -11w + w2 = 60.25 Factor a perfect square on the left side: (w + -5.5)(w + -5.5) = 60.25 Calculate the square root of the right side: 7.762087348 Break this problem into two subproblems by setting (w + -5.5) equal to 7.762087348 and -7.762087348.Subproblem 1
w + -5.5 = 7.762087348 Simplifying w + -5.5 = 7.762087348 Reorder the terms: -5.5 + w = 7.762087348 Solving -5.5 + w = 7.762087348 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + w = 7.762087348 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + w = 7.762087348 + 5.5 w = 7.762087348 + 5.5 Combine like terms: 7.762087348 + 5.5 = 13.262087348 w = 13.262087348 Simplifying w = 13.262087348Subproblem 2
w + -5.5 = -7.762087348 Simplifying w + -5.5 = -7.762087348 Reorder the terms: -5.5 + w = -7.762087348 Solving -5.5 + w = -7.762087348 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + w = -7.762087348 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + w = -7.762087348 + 5.5 w = -7.762087348 + 5.5 Combine like terms: -7.762087348 + 5.5 = -2.262087348 w = -2.262087348 Simplifying w = -2.262087348Solution
The solution to the problem is based on the solutions from the subproblems. w = {13.262087348, -2.262087348}Solution
w = {0, 13.262087348, -2.262087348}
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