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Simplifying 4.43 = 0.0001T2 + 0.0545T + 3.7236 Reorder the terms: 4.43 = 3.7236 + 0.0545T + 0.0001T2 Solving 4.43 = 3.7236 + 0.0545T + 0.0001T2 Solving for variable 'T'. Combine like terms: 4.43 + -3.7236 = 0.7064 0.7064 + -0.0545T + -0.0001T2 = 3.7236 + 0.0545T + 0.0001T2 + -3.7236 + -0.0545T + -0.0001T2 Reorder the terms: 0.7064 + -0.0545T + -0.0001T2 = 3.7236 + -3.7236 + 0.0545T + -0.0545T + 0.0001T2 + -0.0001T2 Combine like terms: 3.7236 + -3.7236 = 0.0000 0.7064 + -0.0545T + -0.0001T2 = 0.0000 + 0.0545T + -0.0545T + 0.0001T2 + -0.0001T2 0.7064 + -0.0545T + -0.0001T2 = 0.0545T + -0.0545T + 0.0001T2 + -0.0001T2 Combine like terms: 0.0545T + -0.0545T = 0.0000 0.7064 + -0.0545T + -0.0001T2 = 0.0000 + 0.0001T2 + -0.0001T2 0.7064 + -0.0545T + -0.0001T2 = 0.0001T2 + -0.0001T2 Combine like terms: 0.0001T2 + -0.0001T2 = 0.0000 0.7064 + -0.0545T + -0.0001T2 = 0.0000 Begin completing the square. Divide all terms by -0.0001 the coefficient of the squared term: Divide each side by '-0.0001'. -7064 + 545T + T2 = 0 Move the constant term to the right: Add '7064' to each side of the equation. -7064 + 545T + 7064 + T2 = 0 + 7064 Reorder the terms: -7064 + 7064 + 545T + T2 = 0 + 7064 Combine like terms: -7064 + 7064 = 0 0 + 545T + T2 = 0 + 7064 545T + T2 = 0 + 7064 Combine like terms: 0 + 7064 = 7064 545T + T2 = 7064 The T term is 545T. Take half its coefficient (272.5). Square it (74256.25) and add it to both sides. Add '74256.25' to each side of the equation. 545T + 74256.25 + T2 = 7064 + 74256.25 Reorder the terms: 74256.25 + 545T + T2 = 7064 + 74256.25 Combine like terms: 7064 + 74256.25 = 81320.25 74256.25 + 545T + T2 = 81320.25 Factor a perfect square on the left side: (T + 272.5)(T + 272.5) = 81320.25 Calculate the square root of the right side: 285.167056302 Break this problem into two subproblems by setting (T + 272.5) equal to 285.167056302 and -285.167056302.Subproblem 1
T + 272.5 = 285.167056302 Simplifying T + 272.5 = 285.167056302 Reorder the terms: 272.5 + T = 285.167056302 Solving 272.5 + T = 285.167056302 Solving for variable 'T'. Move all terms containing T to the left, all other terms to the right. Add '-272.5' to each side of the equation. 272.5 + -272.5 + T = 285.167056302 + -272.5 Combine like terms: 272.5 + -272.5 = 0.0 0.0 + T = 285.167056302 + -272.5 T = 285.167056302 + -272.5 Combine like terms: 285.167056302 + -272.5 = 12.667056302 T = 12.667056302 Simplifying T = 12.667056302Subproblem 2
T + 272.5 = -285.167056302 Simplifying T + 272.5 = -285.167056302 Reorder the terms: 272.5 + T = -285.167056302 Solving 272.5 + T = -285.167056302 Solving for variable 'T'. Move all terms containing T to the left, all other terms to the right. Add '-272.5' to each side of the equation. 272.5 + -272.5 + T = -285.167056302 + -272.5 Combine like terms: 272.5 + -272.5 = 0.0 0.0 + T = -285.167056302 + -272.5 T = -285.167056302 + -272.5 Combine like terms: -285.167056302 + -272.5 = -557.667056302 T = -557.667056302 Simplifying T = -557.667056302Solution
The solution to the problem is based on the solutions from the subproblems. T = {12.667056302, -557.667056302}
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