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Simplifying 260 = (w + 1)(w + 16) Reorder the terms: 260 = (1 + w)(w + 16) Reorder the terms: 260 = (1 + w)(16 + w) Multiply (1 + w) * (16 + w) 260 = (1(16 + w) + w(16 + w)) 260 = ((16 * 1 + w * 1) + w(16 + w)) 260 = ((16 + 1w) + w(16 + w)) 260 = (16 + 1w + (16 * w + w * w)) 260 = (16 + 1w + (16w + w2)) Combine like terms: 1w + 16w = 17w 260 = (16 + 17w + w2) Solving 260 = 16 + 17w + w2 Solving for variable 'w'. Combine like terms: 260 + -16 = 244 244 + -17w + -1w2 = 16 + 17w + w2 + -16 + -17w + -1w2 Reorder the terms: 244 + -17w + -1w2 = 16 + -16 + 17w + -17w + w2 + -1w2 Combine like terms: 16 + -16 = 0 244 + -17w + -1w2 = 0 + 17w + -17w + w2 + -1w2 244 + -17w + -1w2 = 17w + -17w + w2 + -1w2 Combine like terms: 17w + -17w = 0 244 + -17w + -1w2 = 0 + w2 + -1w2 244 + -17w + -1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 244 + -17w + -1w2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -244 + 17w + w2 = 0 Move the constant term to the right: Add '244' to each side of the equation. -244 + 17w + 244 + w2 = 0 + 244 Reorder the terms: -244 + 244 + 17w + w2 = 0 + 244 Combine like terms: -244 + 244 = 0 0 + 17w + w2 = 0 + 244 17w + w2 = 0 + 244 Combine like terms: 0 + 244 = 244 17w + w2 = 244 The w term is 17w. Take half its coefficient (8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. 17w + 72.25 + w2 = 244 + 72.25 Reorder the terms: 72.25 + 17w + w2 = 244 + 72.25 Combine like terms: 244 + 72.25 = 316.25 72.25 + 17w + w2 = 316.25 Factor a perfect square on the left side: (w + 8.5)(w + 8.5) = 316.25 Calculate the square root of the right side: 17.783419244 Break this problem into two subproblems by setting (w + 8.5) equal to 17.783419244 and -17.783419244.Subproblem 1
w + 8.5 = 17.783419244 Simplifying w + 8.5 = 17.783419244 Reorder the terms: 8.5 + w = 17.783419244 Solving 8.5 + w = 17.783419244 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + w = 17.783419244 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + w = 17.783419244 + -8.5 w = 17.783419244 + -8.5 Combine like terms: 17.783419244 + -8.5 = 9.283419244 w = 9.283419244 Simplifying w = 9.283419244Subproblem 2
w + 8.5 = -17.783419244 Simplifying w + 8.5 = -17.783419244 Reorder the terms: 8.5 + w = -17.783419244 Solving 8.5 + w = -17.783419244 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + w = -17.783419244 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + w = -17.783419244 + -8.5 w = -17.783419244 + -8.5 Combine like terms: -17.783419244 + -8.5 = -26.283419244 w = -26.283419244 Simplifying w = -26.283419244Solution
The solution to the problem is based on the solutions from the subproblems. w = {9.283419244, -26.283419244}
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