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Simplifying (w2) + (w + 15) = 1000 w2 + (w + 15) = 1000 Reorder the terms: w2 + (15 + w) = 1000 Remove parenthesis around (15 + w) w2 + 15 + w = 1000 Reorder the terms: 15 + w + w2 = 1000 Solving 15 + w + w2 = 1000 Solving for variable 'w'. Reorder the terms: 15 + -1000 + w + w2 = 1000 + -1000 Combine like terms: 15 + -1000 = -985 -985 + w + w2 = 1000 + -1000 Combine like terms: 1000 + -1000 = 0 -985 + w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '985' to each side of the equation. -985 + w + 985 + w2 = 0 + 985 Reorder the terms: -985 + 985 + w + w2 = 0 + 985 Combine like terms: -985 + 985 = 0 0 + w + w2 = 0 + 985 w + w2 = 0 + 985 Combine like terms: 0 + 985 = 985 w + w2 = 985 The w term is w. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. w + 0.25 + w2 = 985 + 0.25 Reorder the terms: 0.25 + w + w2 = 985 + 0.25 Combine like terms: 985 + 0.25 = 985.25 0.25 + w + w2 = 985.25 Factor a perfect square on the left side: (w + 0.5)(w + 0.5) = 985.25 Calculate the square root of the right side: 31.388692231 Break this problem into two subproblems by setting (w + 0.5) equal to 31.388692231 and -31.388692231.Subproblem 1
w + 0.5 = 31.388692231 Simplifying w + 0.5 = 31.388692231 Reorder the terms: 0.5 + w = 31.388692231 Solving 0.5 + w = 31.388692231 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + w = 31.388692231 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = 31.388692231 + -0.5 w = 31.388692231 + -0.5 Combine like terms: 31.388692231 + -0.5 = 30.888692231 w = 30.888692231 Simplifying w = 30.888692231Subproblem 2
w + 0.5 = -31.388692231 Simplifying w + 0.5 = -31.388692231 Reorder the terms: 0.5 + w = -31.388692231 Solving 0.5 + w = -31.388692231 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + w = -31.388692231 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = -31.388692231 + -0.5 w = -31.388692231 + -0.5 Combine like terms: -31.388692231 + -0.5 = -31.888692231 w = -31.888692231 Simplifying w = -31.888692231Solution
The solution to the problem is based on the solutions from the subproblems. w = {30.888692231, -31.888692231}
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