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Simplifying 0.4285714w2 + -9w + 6 = 0 Reorder the terms: 6 + -9w + 0.4285714w2 = 0 Solving 6 + -9w + 0.4285714w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 0.4285714 the coefficient of the squared term: Divide each side by '0.4285714'. 14.00000093 + -21.0000014w + w2 = 0 Move the constant term to the right: Add '-14.00000093' to each side of the equation. 14.00000093 + -21.0000014w + -14.00000093 + w2 = 0 + -14.00000093 Reorder the terms: 14.00000093 + -14.00000093 + -21.0000014w + w2 = 0 + -14.00000093 Combine like terms: 14.00000093 + -14.00000093 = 0.00000000 0.00000000 + -21.0000014w + w2 = 0 + -14.00000093 -21.0000014w + w2 = 0 + -14.00000093 Combine like terms: 0 + -14.00000093 = -14.00000093 -21.0000014w + w2 = -14.00000093 The w term is -21.0000014w. Take half its coefficient (-10.5000007). Square it (110.2500147) and add it to both sides. Add '110.2500147' to each side of the equation. -21.0000014w + 110.2500147 + w2 = -14.00000093 + 110.2500147 Reorder the terms: 110.2500147 + -21.0000014w + w2 = -14.00000093 + 110.2500147 Combine like terms: -14.00000093 + 110.2500147 = 96.25001377 110.2500147 + -21.0000014w + w2 = 96.25001377 Factor a perfect square on the left side: (w + -10.5000007)(w + -10.5000007) = 96.25001377 Calculate the square root of the right side: 9.810709137 Break this problem into two subproblems by setting (w + -10.5000007) equal to 9.810709137 and -9.810709137.Subproblem 1
w + -10.5000007 = 9.810709137 Simplifying w + -10.5000007 = 9.810709137 Reorder the terms: -10.5000007 + w = 9.810709137 Solving -10.5000007 + w = 9.810709137 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '10.5000007' to each side of the equation. -10.5000007 + 10.5000007 + w = 9.810709137 + 10.5000007 Combine like terms: -10.5000007 + 10.5000007 = 0.0000000 0.0000000 + w = 9.810709137 + 10.5000007 w = 9.810709137 + 10.5000007 Combine like terms: 9.810709137 + 10.5000007 = 20.310709837 w = 20.310709837 Simplifying w = 20.310709837Subproblem 2
w + -10.5000007 = -9.810709137 Simplifying w + -10.5000007 = -9.810709137 Reorder the terms: -10.5000007 + w = -9.810709137 Solving -10.5000007 + w = -9.810709137 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '10.5000007' to each side of the equation. -10.5000007 + 10.5000007 + w = -9.810709137 + 10.5000007 Combine like terms: -10.5000007 + 10.5000007 = 0.0000000 0.0000000 + w = -9.810709137 + 10.5000007 w = -9.810709137 + 10.5000007 Combine like terms: -9.810709137 + 10.5000007 = 0.689291563 w = 0.689291563 Simplifying w = 0.689291563Solution
The solution to the problem is based on the solutions from the subproblems. w = {20.310709837, 0.689291563}
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