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Simplifying 114w = 1 + 1 + 6w2 Combine like terms: 1 + 1 = 2 114w = 2 + 6w2 Solving 114w = 2 + 6w2 Solving for variable 'w'. Reorder the terms: -2 + 114w + -6w2 = 2 + 6w2 + -2 + -6w2 Reorder the terms: -2 + 114w + -6w2 = 2 + -2 + 6w2 + -6w2 Combine like terms: 2 + -2 = 0 -2 + 114w + -6w2 = 0 + 6w2 + -6w2 -2 + 114w + -6w2 = 6w2 + -6w2 Combine like terms: 6w2 + -6w2 = 0 -2 + 114w + -6w2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + 57w + -3w2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + 57w + -3w2)' equal to zero and attempt to solve: Simplifying -1 + 57w + -3w2 = 0 Solving -1 + 57w + -3w2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 0.3333333333 + -19w + w2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + -19w + -0.3333333333 + w2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + -19w + w2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + -19w + w2 = 0 + -0.3333333333 -19w + w2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 -19w + w2 = -0.3333333333 The w term is -19w. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19w + 90.25 + w2 = -0.3333333333 + 90.25 Reorder the terms: 90.25 + -19w + w2 = -0.3333333333 + 90.25 Combine like terms: -0.3333333333 + 90.25 = 89.9166666667 90.25 + -19w + w2 = 89.9166666667 Factor a perfect square on the left side: (w + -9.5)(w + -9.5) = 89.9166666667 Calculate the square root of the right side: 9.482439911 Break this problem into two subproblems by setting (w + -9.5) equal to 9.482439911 and -9.482439911.Subproblem 1
w + -9.5 = 9.482439911 Simplifying w + -9.5 = 9.482439911 Reorder the terms: -9.5 + w = 9.482439911 Solving -9.5 + w = 9.482439911 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + w = 9.482439911 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + w = 9.482439911 + 9.5 w = 9.482439911 + 9.5 Combine like terms: 9.482439911 + 9.5 = 18.982439911 w = 18.982439911 Simplifying w = 18.982439911Subproblem 2
w + -9.5 = -9.482439911 Simplifying w + -9.5 = -9.482439911 Reorder the terms: -9.5 + w = -9.482439911 Solving -9.5 + w = -9.482439911 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + w = -9.482439911 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + w = -9.482439911 + 9.5 w = -9.482439911 + 9.5 Combine like terms: -9.482439911 + 9.5 = 0.017560089 w = 0.017560089 Simplifying w = 0.017560089Solution
The solution to the problem is based on the solutions from the subproblems. w = {18.982439911, 0.017560089}Solution
w = {18.982439911, 0.017560089}
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