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Simplifying 12 = 38T + -4.9T2 Solving 12 = 38T + -4.9T2 Solving for variable 'T'. Reorder the terms: 12 + -38T + 4.9T2 = 38T + -38T + -4.9T2 + 4.9T2 Combine like terms: 38T + -38T = 0 12 + -38T + 4.9T2 = 0 + -4.9T2 + 4.9T2 12 + -38T + 4.9T2 = -4.9T2 + 4.9T2 Combine like terms: -4.9T2 + 4.9T2 = 0.0 12 + -38T + 4.9T2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. 2.448979592 + -7.755102041T + T2 = 0 Move the constant term to the right: Add '-2.448979592' to each side of the equation. 2.448979592 + -7.755102041T + -2.448979592 + T2 = 0 + -2.448979592 Reorder the terms: 2.448979592 + -2.448979592 + -7.755102041T + T2 = 0 + -2.448979592 Combine like terms: 2.448979592 + -2.448979592 = 0.000000000 0.000000000 + -7.755102041T + T2 = 0 + -2.448979592 -7.755102041T + T2 = 0 + -2.448979592 Combine like terms: 0 + -2.448979592 = -2.448979592 -7.755102041T + T2 = -2.448979592 The T term is -7.755102041T. Take half its coefficient (-3.877551021). Square it (15.03540192) and add it to both sides. Add '15.03540192' to each side of the equation. -7.755102041T + 15.03540192 + T2 = -2.448979592 + 15.03540192 Reorder the terms: 15.03540192 + -7.755102041T + T2 = -2.448979592 + 15.03540192 Combine like terms: -2.448979592 + 15.03540192 = 12.586422328 15.03540192 + -7.755102041T + T2 = 12.586422328 Factor a perfect square on the left side: (T + -3.877551021)(T + -3.877551021) = 12.586422328 Calculate the square root of the right side: 3.547734816 Break this problem into two subproblems by setting (T + -3.877551021) equal to 3.547734816 and -3.547734816.Subproblem 1
T + -3.877551021 = 3.547734816 Simplifying T + -3.877551021 = 3.547734816 Reorder the terms: -3.877551021 + T = 3.547734816 Solving -3.877551021 + T = 3.547734816 Solving for variable 'T'. Move all terms containing T to the left, all other terms to the right. Add '3.877551021' to each side of the equation. -3.877551021 + 3.877551021 + T = 3.547734816 + 3.877551021 Combine like terms: -3.877551021 + 3.877551021 = 0.000000000 0.000000000 + T = 3.547734816 + 3.877551021 T = 3.547734816 + 3.877551021 Combine like terms: 3.547734816 + 3.877551021 = 7.425285837 T = 7.425285837 Simplifying T = 7.425285837Subproblem 2
T + -3.877551021 = -3.547734816 Simplifying T + -3.877551021 = -3.547734816 Reorder the terms: -3.877551021 + T = -3.547734816 Solving -3.877551021 + T = -3.547734816 Solving for variable 'T'. Move all terms containing T to the left, all other terms to the right. Add '3.877551021' to each side of the equation. -3.877551021 + 3.877551021 + T = -3.547734816 + 3.877551021 Combine like terms: -3.877551021 + 3.877551021 = 0.000000000 0.000000000 + T = -3.547734816 + 3.877551021 T = -3.547734816 + 3.877551021 Combine like terms: -3.547734816 + 3.877551021 = 0.329816205 T = 0.329816205 Simplifying T = 0.329816205Solution
The solution to the problem is based on the solutions from the subproblems. T = {7.425285837, 0.329816205}
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