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Simplifying 15.87 = 0.0001T2 + 0.0545T + 3.7236 Reorder the terms: 15.87 = 3.7236 + 0.0545T + 0.0001T2 Solving 15.87 = 3.7236 + 0.0545T + 0.0001T2 Solving for variable 'T'. Combine like terms: 15.87 + -3.7236 = 12.1464 12.1464 + -0.0545T + -0.0001T2 = 3.7236 + 0.0545T + 0.0001T2 + -3.7236 + -0.0545T + -0.0001T2 Reorder the terms: 12.1464 + -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 12.1464 + -0.0545T + -0.0001T2 = 0.0000 + 0.0545T + -0.0545T + 0.0001T2 + -0.0001T2 12.1464 + -0.0545T + -0.0001T2 = 0.0545T + -0.0545T + 0.0001T2 + -0.0001T2 Combine like terms: 0.0545T + -0.0545T = 0.0000 12.1464 + -0.0545T + -0.0001T2 = 0.0000 + 0.0001T2 + -0.0001T2 12.1464 + -0.0545T + -0.0001T2 = 0.0001T2 + -0.0001T2 Combine like terms: 0.0001T2 + -0.0001T2 = 0.0000 12.1464 + -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'. -121464 + 545T + T2 = 0 Move the constant term to the right: Add '121464' to each side of the equation. -121464 + 545T + 121464 + T2 = 0 + 121464 Reorder the terms: -121464 + 121464 + 545T + T2 = 0 + 121464 Combine like terms: -121464 + 121464 = 0 0 + 545T + T2 = 0 + 121464 545T + T2 = 0 + 121464 Combine like terms: 0 + 121464 = 121464 545T + T2 = 121464 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 = 121464 + 74256.25 Reorder the terms: 74256.25 + 545T + T2 = 121464 + 74256.25 Combine like terms: 121464 + 74256.25 = 195720.25 74256.25 + 545T + T2 = 195720.25 Factor a perfect square on the left side: (T + 272.5)(T + 272.5) = 195720.25 Calculate the square root of the right side: 442.402814186 Break this problem into two subproblems by setting (T + 272.5) equal to 442.402814186 and -442.402814186.Subproblem 1
T + 272.5 = 442.402814186 Simplifying T + 272.5 = 442.402814186 Reorder the terms: 272.5 + T = 442.402814186 Solving 272.5 + T = 442.402814186 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 = 442.402814186 + -272.5 Combine like terms: 272.5 + -272.5 = 0.0 0.0 + T = 442.402814186 + -272.5 T = 442.402814186 + -272.5 Combine like terms: 442.402814186 + -272.5 = 169.902814186 T = 169.902814186 Simplifying T = 169.902814186Subproblem 2
T + 272.5 = -442.402814186 Simplifying T + 272.5 = -442.402814186 Reorder the terms: 272.5 + T = -442.402814186 Solving 272.5 + T = -442.402814186 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 = -442.402814186 + -272.5 Combine like terms: 272.5 + -272.5 = 0.0 0.0 + T = -442.402814186 + -272.5 T = -442.402814186 + -272.5 Combine like terms: -442.402814186 + -272.5 = -714.902814186 T = -714.902814186 Simplifying T = -714.902814186Solution
The solution to the problem is based on the solutions from the subproblems. T = {169.902814186, -714.902814186}
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