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Simplifying 8w2 + 14w + -17 = 0 Reorder the terms: -17 + 14w + 8w2 = 0 Solving -17 + 14w + 8w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -2.125 + 1.75w + w2 = 0 Move the constant term to the right: Add '2.125' to each side of the equation. -2.125 + 1.75w + 2.125 + w2 = 0 + 2.125 Reorder the terms: -2.125 + 2.125 + 1.75w + w2 = 0 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + 1.75w + w2 = 0 + 2.125 1.75w + w2 = 0 + 2.125 Combine like terms: 0 + 2.125 = 2.125 1.75w + w2 = 2.125 The w term is 1.75w. Take half its coefficient (0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. 1.75w + 0.765625 + w2 = 2.125 + 0.765625 Reorder the terms: 0.765625 + 1.75w + w2 = 2.125 + 0.765625 Combine like terms: 2.125 + 0.765625 = 2.890625 0.765625 + 1.75w + w2 = 2.890625 Factor a perfect square on the left side: (w + 0.875)(w + 0.875) = 2.890625 Calculate the square root of the right side: 1.700183814 Break this problem into two subproblems by setting (w + 0.875) equal to 1.700183814 and -1.700183814.Subproblem 1
w + 0.875 = 1.700183814 Simplifying w + 0.875 = 1.700183814 Reorder the terms: 0.875 + w = 1.700183814 Solving 0.875 + w = 1.700183814 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + w = 1.700183814 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + w = 1.700183814 + -0.875 w = 1.700183814 + -0.875 Combine like terms: 1.700183814 + -0.875 = 0.825183814 w = 0.825183814 Simplifying w = 0.825183814Subproblem 2
w + 0.875 = -1.700183814 Simplifying w + 0.875 = -1.700183814 Reorder the terms: 0.875 + w = -1.700183814 Solving 0.875 + w = -1.700183814 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + w = -1.700183814 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + w = -1.700183814 + -0.875 w = -1.700183814 + -0.875 Combine like terms: -1.700183814 + -0.875 = -2.575183814 w = -2.575183814 Simplifying w = -2.575183814Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.825183814, -2.575183814}
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