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Simplifying 2w2 + 34w + -289 = 625 Reorder the terms: -289 + 34w + 2w2 = 625 Solving -289 + 34w + 2w2 = 625 Solving for variable 'w'. Reorder the terms: -289 + -625 + 34w + 2w2 = 625 + -625 Combine like terms: -289 + -625 = -914 -914 + 34w + 2w2 = 625 + -625 Combine like terms: 625 + -625 = 0 -914 + 34w + 2w2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-457 + 17w + w2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-457 + 17w + w2)' equal to zero and attempt to solve: Simplifying -457 + 17w + w2 = 0 Solving -457 + 17w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '457' to each side of the equation. -457 + 17w + 457 + w2 = 0 + 457 Reorder the terms: -457 + 457 + 17w + w2 = 0 + 457 Combine like terms: -457 + 457 = 0 0 + 17w + w2 = 0 + 457 17w + w2 = 0 + 457 Combine like terms: 0 + 457 = 457 17w + w2 = 457 The w term is 17w. Take half its coefficient (8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. 17w + 72.25 + w2 = 457 + 72.25 Reorder the terms: 72.25 + 17w + w2 = 457 + 72.25 Combine like terms: 457 + 72.25 = 529.25 72.25 + 17w + w2 = 529.25 Factor a perfect square on the left side: (w + 8.5)(w + 8.5) = 529.25 Calculate the square root of the right side: 23.005434141 Break this problem into two subproblems by setting (w + 8.5) equal to 23.005434141 and -23.005434141.Subproblem 1
w + 8.5 = 23.005434141 Simplifying w + 8.5 = 23.005434141 Reorder the terms: 8.5 + w = 23.005434141 Solving 8.5 + w = 23.005434141 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + w = 23.005434141 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + w = 23.005434141 + -8.5 w = 23.005434141 + -8.5 Combine like terms: 23.005434141 + -8.5 = 14.505434141 w = 14.505434141 Simplifying w = 14.505434141Subproblem 2
w + 8.5 = -23.005434141 Simplifying w + 8.5 = -23.005434141 Reorder the terms: 8.5 + w = -23.005434141 Solving 8.5 + w = -23.005434141 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + w = -23.005434141 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + w = -23.005434141 + -8.5 w = -23.005434141 + -8.5 Combine like terms: -23.005434141 + -8.5 = -31.505434141 w = -31.505434141 Simplifying w = -31.505434141Solution
The solution to the problem is based on the solutions from the subproblems. w = {14.505434141, -31.505434141}Solution
w = {14.505434141, -31.505434141}
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