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Simplifying 8w2 + -2122w + 20000 = 0 Reorder the terms: 20000 + -2122w + 8w2 = 0 Solving 20000 + -2122w + 8w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2'. 2(10000 + -1061w + 4w2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(10000 + -1061w + 4w2)' equal to zero and attempt to solve: Simplifying 10000 + -1061w + 4w2 = 0 Solving 10000 + -1061w + 4w2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2500 + -265.25w + w2 = 0 Move the constant term to the right: Add '-2500' to each side of the equation. 2500 + -265.25w + -2500 + w2 = 0 + -2500 Reorder the terms: 2500 + -2500 + -265.25w + w2 = 0 + -2500 Combine like terms: 2500 + -2500 = 0 0 + -265.25w + w2 = 0 + -2500 -265.25w + w2 = 0 + -2500 Combine like terms: 0 + -2500 = -2500 -265.25w + w2 = -2500 The w term is -265.25w. Take half its coefficient (-132.625). Square it (17589.39063) and add it to both sides. Add '17589.39063' to each side of the equation. -265.25w + 17589.39063 + w2 = -2500 + 17589.39063 Reorder the terms: 17589.39063 + -265.25w + w2 = -2500 + 17589.39063 Combine like terms: -2500 + 17589.39063 = 15089.39063 17589.39063 + -265.25w + w2 = 15089.39063 Factor a perfect square on the left side: (w + -132.625)(w + -132.625) = 15089.39063 Calculate the square root of the right side: 122.838880775 Break this problem into two subproblems by setting (w + -132.625) equal to 122.838880775 and -122.838880775.Subproblem 1
w + -132.625 = 122.838880775 Simplifying w + -132.625 = 122.838880775 Reorder the terms: -132.625 + w = 122.838880775 Solving -132.625 + w = 122.838880775 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '132.625' to each side of the equation. -132.625 + 132.625 + w = 122.838880775 + 132.625 Combine like terms: -132.625 + 132.625 = 0.000 0.000 + w = 122.838880775 + 132.625 w = 122.838880775 + 132.625 Combine like terms: 122.838880775 + 132.625 = 255.463880775 w = 255.463880775 Simplifying w = 255.463880775Subproblem 2
w + -132.625 = -122.838880775 Simplifying w + -132.625 = -122.838880775 Reorder the terms: -132.625 + w = -122.838880775 Solving -132.625 + w = -122.838880775 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '132.625' to each side of the equation. -132.625 + 132.625 + w = -122.838880775 + 132.625 Combine like terms: -132.625 + 132.625 = 0.000 0.000 + w = -122.838880775 + 132.625 w = -122.838880775 + 132.625 Combine like terms: -122.838880775 + 132.625 = 9.786119225 w = 9.786119225 Simplifying w = 9.786119225Solution
The solution to the problem is based on the solutions from the subproblems. w = {255.463880775, 9.786119225}Solution
w = {255.463880775, 9.786119225}
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