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Simplifying w(w + 11) = 100 Reorder the terms: w(11 + w) = 100 (11 * w + w * w) = 100 (11w + w2) = 100 Solving 11w + w2 = 100 Solving for variable 'w'. Reorder the terms: -100 + 11w + w2 = 100 + -100 Combine like terms: 100 + -100 = 0 -100 + 11w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '100' to each side of the equation. -100 + 11w + 100 + w2 = 0 + 100 Reorder the terms: -100 + 100 + 11w + w2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + 11w + w2 = 0 + 100 11w + w2 = 0 + 100 Combine like terms: 0 + 100 = 100 11w + w2 = 100 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 = 100 + 30.25 Reorder the terms: 30.25 + 11w + w2 = 100 + 30.25 Combine like terms: 100 + 30.25 = 130.25 30.25 + 11w + w2 = 130.25 Factor a perfect square on the left side: (w + 5.5)(w + 5.5) = 130.25 Calculate the square root of the right side: 11.412712211 Break this problem into two subproblems by setting (w + 5.5) equal to 11.412712211 and -11.412712211.Subproblem 1
w + 5.5 = 11.412712211 Simplifying w + 5.5 = 11.412712211 Reorder the terms: 5.5 + w = 11.412712211 Solving 5.5 + w = 11.412712211 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 = 11.412712211 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + w = 11.412712211 + -5.5 w = 11.412712211 + -5.5 Combine like terms: 11.412712211 + -5.5 = 5.912712211 w = 5.912712211 Simplifying w = 5.912712211Subproblem 2
w + 5.5 = -11.412712211 Simplifying w + 5.5 = -11.412712211 Reorder the terms: 5.5 + w = -11.412712211 Solving 5.5 + w = -11.412712211 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 = -11.412712211 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + w = -11.412712211 + -5.5 w = -11.412712211 + -5.5 Combine like terms: -11.412712211 + -5.5 = -16.912712211 w = -16.912712211 Simplifying w = -16.912712211Solution
The solution to the problem is based on the solutions from the subproblems. w = {5.912712211, -16.912712211}
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