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Simplifying 11.8w2 + -20w + 3.2655 = 0 Reorder the terms: 3.2655 + -20w + 11.8w2 = 0 Solving 3.2655 + -20w + 11.8w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 11.8 the coefficient of the squared term: Divide each side by '11.8'. 0.2767372881 + -1.694915254w + w2 = 0 Move the constant term to the right: Add '-0.2767372881' to each side of the equation. 0.2767372881 + -1.694915254w + -0.2767372881 + w2 = 0 + -0.2767372881 Reorder the terms: 0.2767372881 + -0.2767372881 + -1.694915254w + w2 = 0 + -0.2767372881 Combine like terms: 0.2767372881 + -0.2767372881 = 0.0000000000 0.0000000000 + -1.694915254w + w2 = 0 + -0.2767372881 -1.694915254w + w2 = 0 + -0.2767372881 Combine like terms: 0 + -0.2767372881 = -0.2767372881 -1.694915254w + w2 = -0.2767372881 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 = -0.2767372881 + 0.7181844296 Reorder the terms: 0.7181844296 + -1.694915254w + w2 = -0.2767372881 + 0.7181844296 Combine like terms: -0.2767372881 + 0.7181844296 = 0.4414471415 0.7181844296 + -1.694915254w + w2 = 0.4414471415 Factor a perfect square on the left side: (w + -0.847457627)(w + -0.847457627) = 0.4414471415 Calculate the square root of the right side: 0.664414887 Break this problem into two subproblems by setting (w + -0.847457627) equal to 0.664414887 and -0.664414887.Subproblem 1
w + -0.847457627 = 0.664414887 Simplifying w + -0.847457627 = 0.664414887 Reorder the terms: -0.847457627 + w = 0.664414887 Solving -0.847457627 + w = 0.664414887 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 = 0.664414887 + 0.847457627 Combine like terms: -0.847457627 + 0.847457627 = 0.000000000 0.000000000 + w = 0.664414887 + 0.847457627 w = 0.664414887 + 0.847457627 Combine like terms: 0.664414887 + 0.847457627 = 1.511872514 w = 1.511872514 Simplifying w = 1.511872514Subproblem 2
w + -0.847457627 = -0.664414887 Simplifying w + -0.847457627 = -0.664414887 Reorder the terms: -0.847457627 + w = -0.664414887 Solving -0.847457627 + w = -0.664414887 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 = -0.664414887 + 0.847457627 Combine like terms: -0.847457627 + 0.847457627 = 0.000000000 0.000000000 + w = -0.664414887 + 0.847457627 w = -0.664414887 + 0.847457627 Combine like terms: -0.664414887 + 0.847457627 = 0.18304274 w = 0.18304274 Simplifying w = 0.18304274Solution
The solution to the problem is based on the solutions from the subproblems. w = {1.511872514, 0.18304274}
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