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Simplifying w2 + 11w + -200 = 0 Reorder the terms: -200 + 11w + w2 = 0 Solving -200 + 11w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '200' to each side of the equation. -200 + 11w + 200 + w2 = 0 + 200 Reorder the terms: -200 + 200 + 11w + w2 = 0 + 200 Combine like terms: -200 + 200 = 0 0 + 11w + w2 = 0 + 200 11w + w2 = 0 + 200 Combine like terms: 0 + 200 = 200 11w + w2 = 200 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 = 200 + 30.25 Reorder the terms: 30.25 + 11w + w2 = 200 + 30.25 Combine like terms: 200 + 30.25 = 230.25 30.25 + 11w + w2 = 230.25 Factor a perfect square on the left side: (w + 5.5)(w + 5.5) = 230.25 Calculate the square root of the right side: 15.173990905 Break this problem into two subproblems by setting (w + 5.5) equal to 15.173990905 and -15.173990905.Subproblem 1
w + 5.5 = 15.173990905 Simplifying w + 5.5 = 15.173990905 Reorder the terms: 5.5 + w = 15.173990905 Solving 5.5 + w = 15.173990905 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 = 15.173990905 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + w = 15.173990905 + -5.5 w = 15.173990905 + -5.5 Combine like terms: 15.173990905 + -5.5 = 9.673990905 w = 9.673990905 Simplifying w = 9.673990905Subproblem 2
w + 5.5 = -15.173990905 Simplifying w + 5.5 = -15.173990905 Reorder the terms: 5.5 + w = -15.173990905 Solving 5.5 + w = -15.173990905 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 = -15.173990905 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + w = -15.173990905 + -5.5 w = -15.173990905 + -5.5 Combine like terms: -15.173990905 + -5.5 = -20.673990905 w = -20.673990905 Simplifying w = -20.673990905Solution
The solution to the problem is based on the solutions from the subproblems. w = {9.673990905, -20.673990905}
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