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Simplifying 2w2 + 18w + -174 = 0 Reorder the terms: -174 + 18w + 2w2 = 0 Solving -174 + 18w + 2w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2'. 2(-87 + 9w + w2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-87 + 9w + w2)' equal to zero and attempt to solve: Simplifying -87 + 9w + w2 = 0 Solving -87 + 9w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '87' to each side of the equation. -87 + 9w + 87 + w2 = 0 + 87 Reorder the terms: -87 + 87 + 9w + w2 = 0 + 87 Combine like terms: -87 + 87 = 0 0 + 9w + w2 = 0 + 87 9w + w2 = 0 + 87 Combine like terms: 0 + 87 = 87 9w + w2 = 87 The w term is 9w. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9w + 20.25 + w2 = 87 + 20.25 Reorder the terms: 20.25 + 9w + w2 = 87 + 20.25 Combine like terms: 87 + 20.25 = 107.25 20.25 + 9w + w2 = 107.25 Factor a perfect square on the left side: (w + 4.5)(w + 4.5) = 107.25 Calculate the square root of the right side: 10.356157589 Break this problem into two subproblems by setting (w + 4.5) equal to 10.356157589 and -10.356157589.Subproblem 1
w + 4.5 = 10.356157589 Simplifying w + 4.5 = 10.356157589 Reorder the terms: 4.5 + w = 10.356157589 Solving 4.5 + w = 10.356157589 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + w = 10.356157589 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + w = 10.356157589 + -4.5 w = 10.356157589 + -4.5 Combine like terms: 10.356157589 + -4.5 = 5.856157589 w = 5.856157589 Simplifying w = 5.856157589Subproblem 2
w + 4.5 = -10.356157589 Simplifying w + 4.5 = -10.356157589 Reorder the terms: 4.5 + w = -10.356157589 Solving 4.5 + w = -10.356157589 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + w = -10.356157589 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + w = -10.356157589 + -4.5 w = -10.356157589 + -4.5 Combine like terms: -10.356157589 + -4.5 = -14.856157589 w = -14.856157589 Simplifying w = -14.856157589Solution
The solution to the problem is based on the solutions from the subproblems. w = {5.856157589, -14.856157589}Solution
w = {5.856157589, -14.856157589}
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