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Simplifying w2 + -2w + -200 = 0 Reorder the terms: -200 + -2w + w2 = 0 Solving -200 + -2w + 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 + -2w + 200 + w2 = 0 + 200 Reorder the terms: -200 + 200 + -2w + w2 = 0 + 200 Combine like terms: -200 + 200 = 0 0 + -2w + w2 = 0 + 200 -2w + w2 = 0 + 200 Combine like terms: 0 + 200 = 200 -2w + w2 = 200 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 = 200 + 1 Reorder the terms: 1 + -2w + w2 = 200 + 1 Combine like terms: 200 + 1 = 201 1 + -2w + w2 = 201 Factor a perfect square on the left side: (w + -1)(w + -1) = 201 Calculate the square root of the right side: 14.177446879 Break this problem into two subproblems by setting (w + -1) equal to 14.177446879 and -14.177446879.Subproblem 1
w + -1 = 14.177446879 Simplifying w + -1 = 14.177446879 Reorder the terms: -1 + w = 14.177446879 Solving -1 + w = 14.177446879 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 = 14.177446879 + 1 Combine like terms: -1 + 1 = 0 0 + w = 14.177446879 + 1 w = 14.177446879 + 1 Combine like terms: 14.177446879 + 1 = 15.177446879 w = 15.177446879 Simplifying w = 15.177446879Subproblem 2
w + -1 = -14.177446879 Simplifying w + -1 = -14.177446879 Reorder the terms: -1 + w = -14.177446879 Solving -1 + w = -14.177446879 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 = -14.177446879 + 1 Combine like terms: -1 + 1 = 0 0 + w = -14.177446879 + 1 w = -14.177446879 + 1 Combine like terms: -14.177446879 + 1 = -13.177446879 w = -13.177446879 Simplifying w = -13.177446879Solution
The solution to the problem is based on the solutions from the subproblems. w = {15.177446879, -13.177446879}
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