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Simplifying 0.025 = w(1 + -0.59w) 0.025 = (1 * w + -0.59w * w) 0.025 = (1w + -0.59w2) Solving 0.025 = 1w + -0.59w2 Solving for variable 'w'. Reorder the terms: 0.025 + -1w + 0.59w2 = 1w + -1w + -0.59w2 + 0.59w2 Combine like terms: 1w + -1w = 0 0.025 + -1w + 0.59w2 = 0 + -0.59w2 + 0.59w2 0.025 + -1w + 0.59w2 = -0.59w2 + 0.59w2 Combine like terms: -0.59w2 + 0.59w2 = 0.00 0.025 + -1w + 0.59w2 = 0.00 Begin completing the square. Divide all terms by 0.59 the coefficient of the squared term: Divide each side by '0.59'. 0.04237288136 + -1.694915254w + w2 = 0 Move the constant term to the right: Add '-0.04237288136' to each side of the equation. 0.04237288136 + -1.694915254w + -0.04237288136 + w2 = 0 + -0.04237288136 Reorder the terms: 0.04237288136 + -0.04237288136 + -1.694915254w + w2 = 0 + -0.04237288136 Combine like terms: 0.04237288136 + -0.04237288136 = 0.00000000000 0.00000000000 + -1.694915254w + w2 = 0 + -0.04237288136 -1.694915254w + w2 = 0 + -0.04237288136 Combine like terms: 0 + -0.04237288136 = -0.04237288136 -1.694915254w + w2 = -0.04237288136 The w term is -1.694915254w. Take half its coefficient (-0.847457627). Square it (0.7181844296) and add it to both sides. Add '0.7181844296' to each side of the equation. -1.694915254w + 0.7181844296 + w2 = -0.04237288136 + 0.7181844296 Reorder the terms: 0.7181844296 + -1.694915254w + w2 = -0.04237288136 + 0.7181844296 Combine like terms: -0.04237288136 + 0.7181844296 = 0.67581154824 0.7181844296 + -1.694915254w + w2 = 0.67581154824 Factor a perfect square on the left side: (w + -0.847457627)(w + -0.847457627) = 0.67581154824 Calculate the square root of the right side: 0.82207758 Break this problem into two subproblems by setting (w + -0.847457627) equal to 0.82207758 and -0.82207758.Subproblem 1
w + -0.847457627 = 0.82207758 Simplifying w + -0.847457627 = 0.82207758 Reorder the terms: -0.847457627 + w = 0.82207758 Solving -0.847457627 + w = 0.82207758 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.847457627' to each side of the equation. -0.847457627 + 0.847457627 + w = 0.82207758 + 0.847457627 Combine like terms: -0.847457627 + 0.847457627 = 0.000000000 0.000000000 + w = 0.82207758 + 0.847457627 w = 0.82207758 + 0.847457627 Combine like terms: 0.82207758 + 0.847457627 = 1.669535207 w = 1.669535207 Simplifying w = 1.669535207Subproblem 2
w + -0.847457627 = -0.82207758 Simplifying w + -0.847457627 = -0.82207758 Reorder the terms: -0.847457627 + w = -0.82207758 Solving -0.847457627 + w = -0.82207758 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '0.847457627' to each side of the equation. -0.847457627 + 0.847457627 + w = -0.82207758 + 0.847457627 Combine like terms: -0.847457627 + 0.847457627 = 0.000000000 0.000000000 + w = -0.82207758 + 0.847457627 w = -0.82207758 + 0.847457627 Combine like terms: -0.82207758 + 0.847457627 = 0.025380047 w = 0.025380047 Simplifying w = 0.025380047Solution
The solution to the problem is based on the solutions from the subproblems. w = {1.669535207, 0.025380047}
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