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Simplifying 8.57 = 0.021T2 + 0.296T + 3.803 Reorder the terms: 8.57 = 3.803 + 0.296T + 0.021T2 Solving 8.57 = 3.803 + 0.296T + 0.021T2 Solving for variable 'T'. Combine like terms: 8.57 + -3.803 = 4.767 4.767 + -0.296T + -0.021T2 = 3.803 + 0.296T + 0.021T2 + -3.803 + -0.296T + -0.021T2 Reorder the terms: 4.767 + -0.296T + -0.021T2 = 3.803 + -3.803 + 0.296T + -0.296T + 0.021T2 + -0.021T2 Combine like terms: 3.803 + -3.803 = 0.000 4.767 + -0.296T + -0.021T2 = 0.000 + 0.296T + -0.296T + 0.021T2 + -0.021T2 4.767 + -0.296T + -0.021T2 = 0.296T + -0.296T + 0.021T2 + -0.021T2 Combine like terms: 0.296T + -0.296T = 0.000 4.767 + -0.296T + -0.021T2 = 0.000 + 0.021T2 + -0.021T2 4.767 + -0.296T + -0.021T2 = 0.021T2 + -0.021T2 Combine like terms: 0.021T2 + -0.021T2 = 0.000 4.767 + -0.296T + -0.021T2 = 0.000 Begin completing the square. Divide all terms by -0.021 the coefficient of the squared term: Divide each side by '-0.021'. -227 + 14.0952381T + T2 = 0 Move the constant term to the right: Add '227' to each side of the equation. -227 + 14.0952381T + 227 + T2 = 0 + 227 Reorder the terms: -227 + 227 + 14.0952381T + T2 = 0 + 227 Combine like terms: -227 + 227 = 0 0 + 14.0952381T + T2 = 0 + 227 14.0952381T + T2 = 0 + 227 Combine like terms: 0 + 227 = 227 14.0952381T + T2 = 227 The T term is 14.0952381T. Take half its coefficient (7.04761905). Square it (49.66893427) and add it to both sides. Add '49.66893427' to each side of the equation. 14.0952381T + 49.66893427 + T2 = 227 + 49.66893427 Reorder the terms: 49.66893427 + 14.0952381T + T2 = 227 + 49.66893427 Combine like terms: 227 + 49.66893427 = 276.66893427 49.66893427 + 14.0952381T + T2 = 276.66893427 Factor a perfect square on the left side: (T + 7.04761905)(T + 7.04761905) = 276.66893427 Calculate the square root of the right side: 16.633368098 Break this problem into two subproblems by setting (T + 7.04761905) equal to 16.633368098 and -16.633368098.Subproblem 1
T + 7.04761905 = 16.633368098 Simplifying T + 7.04761905 = 16.633368098 Reorder the terms: 7.04761905 + T = 16.633368098 Solving 7.04761905 + T = 16.633368098 Solving for variable 'T'. Move all terms containing T to the left, all other terms to the right. Add '-7.04761905' to each side of the equation. 7.04761905 + -7.04761905 + T = 16.633368098 + -7.04761905 Combine like terms: 7.04761905 + -7.04761905 = 0.00000000 0.00000000 + T = 16.633368098 + -7.04761905 T = 16.633368098 + -7.04761905 Combine like terms: 16.633368098 + -7.04761905 = 9.585749048 T = 9.585749048 Simplifying T = 9.585749048Subproblem 2
T + 7.04761905 = -16.633368098 Simplifying T + 7.04761905 = -16.633368098 Reorder the terms: 7.04761905 + T = -16.633368098 Solving 7.04761905 + T = -16.633368098 Solving for variable 'T'. Move all terms containing T to the left, all other terms to the right. Add '-7.04761905' to each side of the equation. 7.04761905 + -7.04761905 + T = -16.633368098 + -7.04761905 Combine like terms: 7.04761905 + -7.04761905 = 0.00000000 0.00000000 + T = -16.633368098 + -7.04761905 T = -16.633368098 + -7.04761905 Combine like terms: -16.633368098 + -7.04761905 = -23.680987148 T = -23.680987148 Simplifying T = -23.680987148Solution
The solution to the problem is based on the solutions from the subproblems. T = {9.585749048, -23.680987148}
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