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Simplifying 0 = 4950 + 11w + -1113.75w2 Solving 0 = 4950 + 11w + -1113.75w2 Solving for variable 'w'. Combine like terms: 0 + -4950 = -4950 -4950 + -11w + 1113.75w2 = 4950 + 11w + -1113.75w2 + -4950 + -11w + 1113.75w2 Reorder the terms: -4950 + -11w + 1113.75w2 = 4950 + -4950 + 11w + -11w + -1113.75w2 + 1113.75w2 Combine like terms: 4950 + -4950 = 0 -4950 + -11w + 1113.75w2 = 0 + 11w + -11w + -1113.75w2 + 1113.75w2 -4950 + -11w + 1113.75w2 = 11w + -11w + -1113.75w2 + 1113.75w2 Combine like terms: 11w + -11w = 0 -4950 + -11w + 1113.75w2 = 0 + -1113.75w2 + 1113.75w2 -4950 + -11w + 1113.75w2 = -1113.75w2 + 1113.75w2 Combine like terms: -1113.75w2 + 1113.75w2 = 0.00 -4950 + -11w + 1113.75w2 = 0.00 Begin completing the square. Divide all terms by 1113.75 the coefficient of the squared term: Divide each side by '1113.75'. -4.444444444 + -0.00987654321w + w2 = 0 Move the constant term to the right: Add '4.444444444' to each side of the equation. -4.444444444 + -0.00987654321w + 4.444444444 + w2 = 0 + 4.444444444 Reorder the terms: -4.444444444 + 4.444444444 + -0.00987654321w + w2 = 0 + 4.444444444 Combine like terms: -4.444444444 + 4.444444444 = 0.000000000 0.000000000 + -0.00987654321w + w2 = 0 + 4.444444444 -0.00987654321w + w2 = 0 + 4.444444444 Combine like terms: 0 + 4.444444444 = 4.444444444 -0.00987654321w + w2 = 4.444444444 The w term is -0.00987654321w. Take half its coefficient (-0.004938271605). Square it (0.00002438652644) and add it to both sides. Add '0.00002438652644' to each side of the equation. -0.00987654321w + 0.00002438652644 + w2 = 4.444444444 + 0.00002438652644 Reorder the terms: 0.00002438652644 + -0.00987654321w + w2 = 4.444444444 + 0.00002438652644 Combine like terms: 4.444444444 + 0.00002438652644 = 4.44446883052644 0.00002438652644 + -0.00987654321w + w2 = 4.44446883052644 Factor a perfect square on the left side: (w + -0.004938271605)(w + -0.004938271605) = 4.44446883052644 Calculate the square root of the right side: 2.10819089 Break this problem into two subproblems by setting (w + -0.004938271605) equal to 2.10819089 and -2.10819089.Subproblem 1
w + -0.004938271605 = 2.10819089 Simplifying w + -0.004938271605 = 2.10819089 Reorder the terms: -0.004938271605 + w = 2.10819089 Solving -0.004938271605 + w = 2.10819089 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.004938271605' to each side of the equation. -0.004938271605 + 0.004938271605 + w = 2.10819089 + 0.004938271605 Combine like terms: -0.004938271605 + 0.004938271605 = 0.000000000000 0.000000000000 + w = 2.10819089 + 0.004938271605 w = 2.10819089 + 0.004938271605 Combine like terms: 2.10819089 + 0.004938271605 = 2.113129161605 w = 2.113129161605 Simplifying w = 2.113129161605Subproblem 2
w + -0.004938271605 = -2.10819089 Simplifying w + -0.004938271605 = -2.10819089 Reorder the terms: -0.004938271605 + w = -2.10819089 Solving -0.004938271605 + w = -2.10819089 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.004938271605' to each side of the equation. -0.004938271605 + 0.004938271605 + w = -2.10819089 + 0.004938271605 Combine like terms: -0.004938271605 + 0.004938271605 = 0.000000000000 0.000000000000 + w = -2.10819089 + 0.004938271605 w = -2.10819089 + 0.004938271605 Combine like terms: -2.10819089 + 0.004938271605 = -2.103252618395 w = -2.103252618395 Simplifying w = -2.103252618395Solution
The solution to the problem is based on the solutions from the subproblems. w = {2.113129161605, -2.103252618395}
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