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Simplifying 2w2 + -6w = 104 Reorder the terms: -6w + 2w2 = 104 Solving -6w + 2w2 = 104 Solving for variable 'w'. Reorder the terms: -104 + -6w + 2w2 = 104 + -104 Combine like terms: 104 + -104 = 0 -104 + -6w + 2w2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-52 + -3w + w2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-52 + -3w + w2)' equal to zero and attempt to solve: Simplifying -52 + -3w + w2 = 0 Solving -52 + -3w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '52' to each side of the equation. -52 + -3w + 52 + w2 = 0 + 52 Reorder the terms: -52 + 52 + -3w + w2 = 0 + 52 Combine like terms: -52 + 52 = 0 0 + -3w + w2 = 0 + 52 -3w + w2 = 0 + 52 Combine like terms: 0 + 52 = 52 -3w + w2 = 52 The w term is -3w. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3w + 2.25 + w2 = 52 + 2.25 Reorder the terms: 2.25 + -3w + w2 = 52 + 2.25 Combine like terms: 52 + 2.25 = 54.25 2.25 + -3w + w2 = 54.25 Factor a perfect square on the left side: (w + -1.5)(w + -1.5) = 54.25 Calculate the square root of the right side: 7.365459931 Break this problem into two subproblems by setting (w + -1.5) equal to 7.365459931 and -7.365459931.Subproblem 1
w + -1.5 = 7.365459931 Simplifying w + -1.5 = 7.365459931 Reorder the terms: -1.5 + w = 7.365459931 Solving -1.5 + w = 7.365459931 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + w = 7.365459931 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + w = 7.365459931 + 1.5 w = 7.365459931 + 1.5 Combine like terms: 7.365459931 + 1.5 = 8.865459931 w = 8.865459931 Simplifying w = 8.865459931Subproblem 2
w + -1.5 = -7.365459931 Simplifying w + -1.5 = -7.365459931 Reorder the terms: -1.5 + w = -7.365459931 Solving -1.5 + w = -7.365459931 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + w = -7.365459931 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + w = -7.365459931 + 1.5 w = -7.365459931 + 1.5 Combine like terms: -7.365459931 + 1.5 = -5.865459931 w = -5.865459931 Simplifying w = -5.865459931Solution
The solution to the problem is based on the solutions from the subproblems. w = {8.865459931, -5.865459931}Solution
w = {8.865459931, -5.865459931}
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