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Simplifying 3T2 + -92T + 12 = 0 Reorder the terms: 12 + -92T + 3T2 = 0 Solving 12 + -92T + 3T2 = 0 Solving for variable 'T'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 4 + -30.66666667T + T2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -30.66666667T + -4 + T2 = 0 + -4 Reorder the terms: 4 + -4 + -30.66666667T + T2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -30.66666667T + T2 = 0 + -4 -30.66666667T + T2 = 0 + -4 Combine like terms: 0 + -4 = -4 -30.66666667T + T2 = -4 The T term is -30.66666667T. Take half its coefficient (-15.33333334). Square it (235.1111113) and add it to both sides. Add '235.1111113' to each side of the equation. -30.66666667T + 235.1111113 + T2 = -4 + 235.1111113 Reorder the terms: 235.1111113 + -30.66666667T + T2 = -4 + 235.1111113 Combine like terms: -4 + 235.1111113 = 231.1111113 235.1111113 + -30.66666667T + T2 = 231.1111113 Factor a perfect square on the left side: (T + -15.33333334)(T + -15.33333334) = 231.1111113 Calculate the square root of the right side: 15.202339008 Break this problem into two subproblems by setting (T + -15.33333334) equal to 15.202339008 and -15.202339008.Subproblem 1
T + -15.33333334 = 15.202339008 Simplifying T + -15.33333334 = 15.202339008 Reorder the terms: -15.33333334 + T = 15.202339008 Solving -15.33333334 + T = 15.202339008 Solving for variable 'T'. Move all terms containing T to the left, all other terms to the right. Add '15.33333334' to each side of the equation. -15.33333334 + 15.33333334 + T = 15.202339008 + 15.33333334 Combine like terms: -15.33333334 + 15.33333334 = 0.00000000 0.00000000 + T = 15.202339008 + 15.33333334 T = 15.202339008 + 15.33333334 Combine like terms: 15.202339008 + 15.33333334 = 30.535672348 T = 30.535672348 Simplifying T = 30.535672348Subproblem 2
T + -15.33333334 = -15.202339008 Simplifying T + -15.33333334 = -15.202339008 Reorder the terms: -15.33333334 + T = -15.202339008 Solving -15.33333334 + T = -15.202339008 Solving for variable 'T'. Move all terms containing T to the left, all other terms to the right. Add '15.33333334' to each side of the equation. -15.33333334 + 15.33333334 + T = -15.202339008 + 15.33333334 Combine like terms: -15.33333334 + 15.33333334 = 0.00000000 0.00000000 + T = -15.202339008 + 15.33333334 T = -15.202339008 + 15.33333334 Combine like terms: -15.202339008 + 15.33333334 = 0.130994332 T = 0.130994332 Simplifying T = 0.130994332Solution
The solution to the problem is based on the solutions from the subproblems. T = {30.535672348, 0.130994332}
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