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Simplifying 2w(w + -2) = 170 Reorder the terms: 2w(-2 + w) = 170 (-2 * 2w + w * 2w) = 170 (-4w + 2w2) = 170 Solving -4w + 2w2 = 170 Solving for variable 'w'. Reorder the terms: -170 + -4w + 2w2 = 170 + -170 Combine like terms: 170 + -170 = 0 -170 + -4w + 2w2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-85 + -2w + w2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-85 + -2w + w2)' equal to zero and attempt to solve: Simplifying -85 + -2w + w2 = 0 Solving -85 + -2w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '85' to each side of the equation. -85 + -2w + 85 + w2 = 0 + 85 Reorder the terms: -85 + 85 + -2w + w2 = 0 + 85 Combine like terms: -85 + 85 = 0 0 + -2w + w2 = 0 + 85 -2w + w2 = 0 + 85 Combine like terms: 0 + 85 = 85 -2w + w2 = 85 The w term is -2w. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2w + 1 + w2 = 85 + 1 Reorder the terms: 1 + -2w + w2 = 85 + 1 Combine like terms: 85 + 1 = 86 1 + -2w + w2 = 86 Factor a perfect square on the left side: (w + -1)(w + -1) = 86 Calculate the square root of the right side: 9.273618495 Break this problem into two subproblems by setting (w + -1) equal to 9.273618495 and -9.273618495.Subproblem 1
w + -1 = 9.273618495 Simplifying w + -1 = 9.273618495 Reorder the terms: -1 + w = 9.273618495 Solving -1 + w = 9.273618495 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + w = 9.273618495 + 1 Combine like terms: -1 + 1 = 0 0 + w = 9.273618495 + 1 w = 9.273618495 + 1 Combine like terms: 9.273618495 + 1 = 10.273618495 w = 10.273618495 Simplifying w = 10.273618495Subproblem 2
w + -1 = -9.273618495 Simplifying w + -1 = -9.273618495 Reorder the terms: -1 + w = -9.273618495 Solving -1 + w = -9.273618495 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + w = -9.273618495 + 1 Combine like terms: -1 + 1 = 0 0 + w = -9.273618495 + 1 w = -9.273618495 + 1 Combine like terms: -9.273618495 + 1 = -8.273618495 w = -8.273618495 Simplifying w = -8.273618495Solution
The solution to the problem is based on the solutions from the subproblems. w = {10.273618495, -8.273618495}Solution
w = {10.273618495, -8.273618495}
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