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Simplifying 1.256L2 + 35.3L + 27.98 = 625 Reorder the terms: 27.98 + 35.3L + 1.256L2 = 625 Solving 27.98 + 35.3L + 1.256L2 = 625 Solving for variable 'L'. Reorder the terms: 27.98 + -625 + 35.3L + 1.256L2 = 625 + -625 Combine like terms: 27.98 + -625 = -597.02 -597.02 + 35.3L + 1.256L2 = 625 + -625 Combine like terms: 625 + -625 = 0 -597.02 + 35.3L + 1.256L2 = 0 Begin completing the square. Divide all terms by 1.256 the coefficient of the squared term: Divide each side by '1.256'. -475.3343949 + 28.10509554L + L2 = 0 Move the constant term to the right: Add '475.3343949' to each side of the equation. -475.3343949 + 28.10509554L + 475.3343949 + L2 = 0 + 475.3343949 Reorder the terms: -475.3343949 + 475.3343949 + 28.10509554L + L2 = 0 + 475.3343949 Combine like terms: -475.3343949 + 475.3343949 = 0.0000000 0.0000000 + 28.10509554L + L2 = 0 + 475.3343949 28.10509554L + L2 = 0 + 475.3343949 Combine like terms: 0 + 475.3343949 = 475.3343949 28.10509554L + L2 = 475.3343949 The L term is 28.10509554L. Take half its coefficient (14.05254777). Square it (197.4740988) and add it to both sides. Add '197.4740988' to each side of the equation. 28.10509554L + 197.4740988 + L2 = 475.3343949 + 197.4740988 Reorder the terms: 197.4740988 + 28.10509554L + L2 = 475.3343949 + 197.4740988 Combine like terms: 475.3343949 + 197.4740988 = 672.8084937 197.4740988 + 28.10509554L + L2 = 672.8084937 Factor a perfect square on the left side: (L + 14.05254777)(L + 14.05254777) = 672.8084937 Calculate the square root of the right side: 25.938552267 Break this problem into two subproblems by setting (L + 14.05254777) equal to 25.938552267 and -25.938552267.Subproblem 1
L + 14.05254777 = 25.938552267 Simplifying L + 14.05254777 = 25.938552267 Reorder the terms: 14.05254777 + L = 25.938552267 Solving 14.05254777 + L = 25.938552267 Solving for variable 'L'. Move all terms containing L to the left, all other terms to the right. Add '-14.05254777' to each side of the equation. 14.05254777 + -14.05254777 + L = 25.938552267 + -14.05254777 Combine like terms: 14.05254777 + -14.05254777 = 0.00000000 0.00000000 + L = 25.938552267 + -14.05254777 L = 25.938552267 + -14.05254777 Combine like terms: 25.938552267 + -14.05254777 = 11.886004497 L = 11.886004497 Simplifying L = 11.886004497Subproblem 2
L + 14.05254777 = -25.938552267 Simplifying L + 14.05254777 = -25.938552267 Reorder the terms: 14.05254777 + L = -25.938552267 Solving 14.05254777 + L = -25.938552267 Solving for variable 'L'. Move all terms containing L to the left, all other terms to the right. Add '-14.05254777' to each side of the equation. 14.05254777 + -14.05254777 + L = -25.938552267 + -14.05254777 Combine like terms: 14.05254777 + -14.05254777 = 0.00000000 0.00000000 + L = -25.938552267 + -14.05254777 L = -25.938552267 + -14.05254777 Combine like terms: -25.938552267 + -14.05254777 = -39.991100037 L = -39.991100037 Simplifying L = -39.991100037Solution
The solution to the problem is based on the solutions from the subproblems. L = {11.886004497, -39.991100037}
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