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Simplifying (w + 11)(w) = 130 Reorder the terms: (11 + w)(w) = 130 Reorder the terms for easier multiplication: w(11 + w) = 130 (11 * w + w * w) = 130 (11w + w2) = 130 Solving 11w + w2 = 130 Solving for variable 'w'. Reorder the terms: -130 + 11w + w2 = 130 + -130 Combine like terms: 130 + -130 = 0 -130 + 11w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '130' to each side of the equation. -130 + 11w + 130 + w2 = 0 + 130 Reorder the terms: -130 + 130 + 11w + w2 = 0 + 130 Combine like terms: -130 + 130 = 0 0 + 11w + w2 = 0 + 130 11w + w2 = 0 + 130 Combine like terms: 0 + 130 = 130 11w + w2 = 130 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 = 130 + 30.25 Reorder the terms: 30.25 + 11w + w2 = 130 + 30.25 Combine like terms: 130 + 30.25 = 160.25 30.25 + 11w + w2 = 160.25 Factor a perfect square on the left side: (w + 5.5)(w + 5.5) = 160.25 Calculate the square root of the right side: 12.658988901 Break this problem into two subproblems by setting (w + 5.5) equal to 12.658988901 and -12.658988901.Subproblem 1
w + 5.5 = 12.658988901 Simplifying w + 5.5 = 12.658988901 Reorder the terms: 5.5 + w = 12.658988901 Solving 5.5 + w = 12.658988901 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 = 12.658988901 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + w = 12.658988901 + -5.5 w = 12.658988901 + -5.5 Combine like terms: 12.658988901 + -5.5 = 7.158988901 w = 7.158988901 Simplifying w = 7.158988901Subproblem 2
w + 5.5 = -12.658988901 Simplifying w + 5.5 = -12.658988901 Reorder the terms: 5.5 + w = -12.658988901 Solving 5.5 + w = -12.658988901 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 = -12.658988901 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + w = -12.658988901 + -5.5 w = -12.658988901 + -5.5 Combine like terms: -12.658988901 + -5.5 = -18.158988901 w = -18.158988901 Simplifying w = -18.158988901Solution
The solution to the problem is based on the solutions from the subproblems. w = {7.158988901, -18.158988901}
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