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Simplifying -17w + 40 = 8w2 + 5 Reorder the terms: 40 + -17w = 8w2 + 5 Reorder the terms: 40 + -17w = 5 + 8w2 Solving 40 + -17w = 5 + 8w2 Solving for variable 'w'. Reorder the terms: 40 + -5 + -17w + -8w2 = 5 + 8w2 + -5 + -8w2 Combine like terms: 40 + -5 = 35 35 + -17w + -8w2 = 5 + 8w2 + -5 + -8w2 Reorder the terms: 35 + -17w + -8w2 = 5 + -5 + 8w2 + -8w2 Combine like terms: 5 + -5 = 0 35 + -17w + -8w2 = 0 + 8w2 + -8w2 35 + -17w + -8w2 = 8w2 + -8w2 Combine like terms: 8w2 + -8w2 = 0 35 + -17w + -8w2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -4.375 + 2.125w + w2 = 0 Move the constant term to the right: Add '4.375' to each side of the equation. -4.375 + 2.125w + 4.375 + w2 = 0 + 4.375 Reorder the terms: -4.375 + 4.375 + 2.125w + w2 = 0 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + 2.125w + w2 = 0 + 4.375 2.125w + w2 = 0 + 4.375 Combine like terms: 0 + 4.375 = 4.375 2.125w + w2 = 4.375 The w term is 2.125w. Take half its coefficient (1.0625). Square it (1.12890625) and add it to both sides. Add '1.12890625' to each side of the equation. 2.125w + 1.12890625 + w2 = 4.375 + 1.12890625 Reorder the terms: 1.12890625 + 2.125w + w2 = 4.375 + 1.12890625 Combine like terms: 4.375 + 1.12890625 = 5.50390625 1.12890625 + 2.125w + w2 = 5.50390625 Factor a perfect square on the left side: (w + 1.0625)(w + 1.0625) = 5.50390625 Calculate the square root of the right side: 2.346040547 Break this problem into two subproblems by setting (w + 1.0625) equal to 2.346040547 and -2.346040547.Subproblem 1
w + 1.0625 = 2.346040547 Simplifying w + 1.0625 = 2.346040547 Reorder the terms: 1.0625 + w = 2.346040547 Solving 1.0625 + w = 2.346040547 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.0625' to each side of the equation. 1.0625 + -1.0625 + w = 2.346040547 + -1.0625 Combine like terms: 1.0625 + -1.0625 = 0.0000 0.0000 + w = 2.346040547 + -1.0625 w = 2.346040547 + -1.0625 Combine like terms: 2.346040547 + -1.0625 = 1.283540547 w = 1.283540547 Simplifying w = 1.283540547Subproblem 2
w + 1.0625 = -2.346040547 Simplifying w + 1.0625 = -2.346040547 Reorder the terms: 1.0625 + w = -2.346040547 Solving 1.0625 + w = -2.346040547 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.0625' to each side of the equation. 1.0625 + -1.0625 + w = -2.346040547 + -1.0625 Combine like terms: 1.0625 + -1.0625 = 0.0000 0.0000 + w = -2.346040547 + -1.0625 w = -2.346040547 + -1.0625 Combine like terms: -2.346040547 + -1.0625 = -3.408540547 w = -3.408540547 Simplifying w = -3.408540547Solution
The solution to the problem is based on the solutions from the subproblems. w = {1.283540547, -3.408540547}
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