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Simplifying w2 + -2w = 13 Reorder the terms: -2w + w2 = 13 Solving -2w + w2 = 13 Solving for variable 'w'. Reorder the terms: -13 + -2w + w2 = 13 + -13 Combine like terms: 13 + -13 = 0 -13 + -2w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + -2w + 13 + w2 = 0 + 13 Reorder the terms: -13 + 13 + -2w + w2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -2w + w2 = 0 + 13 -2w + w2 = 0 + 13 Combine like terms: 0 + 13 = 13 -2w + w2 = 13 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 = 13 + 1 Reorder the terms: 1 + -2w + w2 = 13 + 1 Combine like terms: 13 + 1 = 14 1 + -2w + w2 = 14 Factor a perfect square on the left side: (w + -1)(w + -1) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (w + -1) equal to 3.741657387 and -3.741657387.Subproblem 1
w + -1 = 3.741657387 Simplifying w + -1 = 3.741657387 Reorder the terms: -1 + w = 3.741657387 Solving -1 + w = 3.741657387 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 = 3.741657387 + 1 Combine like terms: -1 + 1 = 0 0 + w = 3.741657387 + 1 w = 3.741657387 + 1 Combine like terms: 3.741657387 + 1 = 4.741657387 w = 4.741657387 Simplifying w = 4.741657387Subproblem 2
w + -1 = -3.741657387 Simplifying w + -1 = -3.741657387 Reorder the terms: -1 + w = -3.741657387 Solving -1 + w = -3.741657387 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 = -3.741657387 + 1 Combine like terms: -1 + 1 = 0 0 + w = -3.741657387 + 1 w = -3.741657387 + 1 Combine like terms: -3.741657387 + 1 = -2.741657387 w = -2.741657387 Simplifying w = -2.741657387Solution
The solution to the problem is based on the solutions from the subproblems. w = {4.741657387, -2.741657387}
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