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Simplifying T2 + 10T + -102 = 0 Reorder the terms: -102 + 10T + T2 = 0 Solving -102 + 10T + T2 = 0 Solving for variable 'T'. Begin completing the square. Move the constant term to the right: Add '102' to each side of the equation. -102 + 10T + 102 + T2 = 0 + 102 Reorder the terms: -102 + 102 + 10T + T2 = 0 + 102 Combine like terms: -102 + 102 = 0 0 + 10T + T2 = 0 + 102 10T + T2 = 0 + 102 Combine like terms: 0 + 102 = 102 10T + T2 = 102 The T term is 10T. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10T + 25 + T2 = 102 + 25 Reorder the terms: 25 + 10T + T2 = 102 + 25 Combine like terms: 102 + 25 = 127 25 + 10T + T2 = 127 Factor a perfect square on the left side: (T + 5)(T + 5) = 127 Calculate the square root of the right side: 11.26942767 Break this problem into two subproblems by setting (T + 5) equal to 11.26942767 and -11.26942767.Subproblem 1
T + 5 = 11.26942767 Simplifying T + 5 = 11.26942767 Reorder the terms: 5 + T = 11.26942767 Solving 5 + T = 11.26942767 Solving for variable 'T'. Move all terms containing T to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + T = 11.26942767 + -5 Combine like terms: 5 + -5 = 0 0 + T = 11.26942767 + -5 T = 11.26942767 + -5 Combine like terms: 11.26942767 + -5 = 6.26942767 T = 6.26942767 Simplifying T = 6.26942767Subproblem 2
T + 5 = -11.26942767 Simplifying T + 5 = -11.26942767 Reorder the terms: 5 + T = -11.26942767 Solving 5 + T = -11.26942767 Solving for variable 'T'. Move all terms containing T to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + T = -11.26942767 + -5 Combine like terms: 5 + -5 = 0 0 + T = -11.26942767 + -5 T = -11.26942767 + -5 Combine like terms: -11.26942767 + -5 = -16.26942767 T = -16.26942767 Simplifying T = -16.26942767Solution
The solution to the problem is based on the solutions from the subproblems. T = {6.26942767, -16.26942767}
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