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Simplifying w2 + 2w + -310 = 0 Reorder the terms: -310 + 2w + w2 = 0 Solving -310 + 2w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '310' to each side of the equation. -310 + 2w + 310 + w2 = 0 + 310 Reorder the terms: -310 + 310 + 2w + w2 = 0 + 310 Combine like terms: -310 + 310 = 0 0 + 2w + w2 = 0 + 310 2w + w2 = 0 + 310 Combine like terms: 0 + 310 = 310 2w + w2 = 310 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 = 310 + 1 Reorder the terms: 1 + 2w + w2 = 310 + 1 Combine like terms: 310 + 1 = 311 1 + 2w + w2 = 311 Factor a perfect square on the left side: (w + 1)(w + 1) = 311 Calculate the square root of the right side: 17.635192089 Break this problem into two subproblems by setting (w + 1) equal to 17.635192089 and -17.635192089.Subproblem 1
w + 1 = 17.635192089 Simplifying w + 1 = 17.635192089 Reorder the terms: 1 + w = 17.635192089 Solving 1 + w = 17.635192089 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 = 17.635192089 + -1 Combine like terms: 1 + -1 = 0 0 + w = 17.635192089 + -1 w = 17.635192089 + -1 Combine like terms: 17.635192089 + -1 = 16.635192089 w = 16.635192089 Simplifying w = 16.635192089Subproblem 2
w + 1 = -17.635192089 Simplifying w + 1 = -17.635192089 Reorder the terms: 1 + w = -17.635192089 Solving 1 + w = -17.635192089 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 = -17.635192089 + -1 Combine like terms: 1 + -1 = 0 0 + w = -17.635192089 + -1 w = -17.635192089 + -1 Combine like terms: -17.635192089 + -1 = -18.635192089 w = -18.635192089 Simplifying w = -18.635192089Solution
The solution to the problem is based on the solutions from the subproblems. w = {16.635192089, -18.635192089}
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