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Simplifying w2 + 2w + -91 = 0 Reorder the terms: -91 + 2w + w2 = 0 Solving -91 + 2w + w2 = 0 Solving for variable 'w'. Begin completing the square. Move the constant term to the right: Add '91' to each side of the equation. -91 + 2w + 91 + w2 = 0 + 91 Reorder the terms: -91 + 91 + 2w + w2 = 0 + 91 Combine like terms: -91 + 91 = 0 0 + 2w + w2 = 0 + 91 2w + w2 = 0 + 91 Combine like terms: 0 + 91 = 91 2w + w2 = 91 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 = 91 + 1 Reorder the terms: 1 + 2w + w2 = 91 + 1 Combine like terms: 91 + 1 = 92 1 + 2w + w2 = 92 Factor a perfect square on the left side: (w + 1)(w + 1) = 92 Calculate the square root of the right side: 9.591663047 Break this problem into two subproblems by setting (w + 1) equal to 9.591663047 and -9.591663047.Subproblem 1
w + 1 = 9.591663047 Simplifying w + 1 = 9.591663047 Reorder the terms: 1 + w = 9.591663047 Solving 1 + w = 9.591663047 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 = 9.591663047 + -1 Combine like terms: 1 + -1 = 0 0 + w = 9.591663047 + -1 w = 9.591663047 + -1 Combine like terms: 9.591663047 + -1 = 8.591663047 w = 8.591663047 Simplifying w = 8.591663047Subproblem 2
w + 1 = -9.591663047 Simplifying w + 1 = -9.591663047 Reorder the terms: 1 + w = -9.591663047 Solving 1 + w = -9.591663047 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 = -9.591663047 + -1 Combine like terms: 1 + -1 = 0 0 + w = -9.591663047 + -1 w = -9.591663047 + -1 Combine like terms: -9.591663047 + -1 = -10.591663047 w = -10.591663047 Simplifying w = -10.591663047Solution
The solution to the problem is based on the solutions from the subproblems. w = {8.591663047, -10.591663047}
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