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Simplifying 0.0787 = w(1 + -0.59w) 0.0787 = (1 * w + -0.59w * w) 0.0787 = (1w + -0.59w2) Solving 0.0787 = 1w + -0.59w2 Solving for variable 'w'. Reorder the terms: 0.0787 + -1w + 0.59w2 = 1w + -1w + -0.59w2 + 0.59w2 Combine like terms: 1w + -1w = 0 0.0787 + -1w + 0.59w2 = 0 + -0.59w2 + 0.59w2 0.0787 + -1w + 0.59w2 = -0.59w2 + 0.59w2 Combine like terms: -0.59w2 + 0.59w2 = 0.00 0.0787 + -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'. 0.1333898305 + -1.694915254w + w2 = 0 Move the constant term to the right: Add '-0.1333898305' to each side of the equation. 0.1333898305 + -1.694915254w + -0.1333898305 + w2 = 0 + -0.1333898305 Reorder the terms: 0.1333898305 + -0.1333898305 + -1.694915254w + w2 = 0 + -0.1333898305 Combine like terms: 0.1333898305 + -0.1333898305 = 0.0000000000 0.0000000000 + -1.694915254w + w2 = 0 + -0.1333898305 -1.694915254w + w2 = 0 + -0.1333898305 Combine like terms: 0 + -0.1333898305 = -0.1333898305 -1.694915254w + w2 = -0.1333898305 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 = -0.1333898305 + 0.7181844296 Reorder the terms: 0.7181844296 + -1.694915254w + w2 = -0.1333898305 + 0.7181844296 Combine like terms: -0.1333898305 + 0.7181844296 = 0.5847945991 0.7181844296 + -1.694915254w + w2 = 0.5847945991 Factor a perfect square on the left side: (w + -0.847457627)(w + -0.847457627) = 0.5847945991 Calculate the square root of the right side: 0.76471864 Break this problem into two subproblems by setting (w + -0.847457627) equal to 0.76471864 and -0.76471864.Subproblem 1
w + -0.847457627 = 0.76471864 Simplifying w + -0.847457627 = 0.76471864 Reorder the terms: -0.847457627 + w = 0.76471864 Solving -0.847457627 + w = 0.76471864 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 = 0.76471864 + 0.847457627 Combine like terms: -0.847457627 + 0.847457627 = 0.000000000 0.000000000 + w = 0.76471864 + 0.847457627 w = 0.76471864 + 0.847457627 Combine like terms: 0.76471864 + 0.847457627 = 1.612176267 w = 1.612176267 Simplifying w = 1.612176267Subproblem 2
w + -0.847457627 = -0.76471864 Simplifying w + -0.847457627 = -0.76471864 Reorder the terms: -0.847457627 + w = -0.76471864 Solving -0.847457627 + w = -0.76471864 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 = -0.76471864 + 0.847457627 Combine like terms: -0.847457627 + 0.847457627 = 0.000000000 0.000000000 + w = -0.76471864 + 0.847457627 w = -0.76471864 + 0.847457627 Combine like terms: -0.76471864 + 0.847457627 = 0.082738987 w = 0.082738987 Simplifying w = 0.082738987Solution
The solution to the problem is based on the solutions from the subproblems. w = {1.612176267, 0.082738987}
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