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Simplifying 10T + -5T2 = 4 Solving 10T + -5T2 = 4 Solving for variable 'T'. Reorder the terms: -4 + 10T + -5T2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + 10T + -5T2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 0.8 + -2T + T2 = 0 Move the constant term to the right: Add '-0.8' to each side of the equation. 0.8 + -2T + -0.8 + T2 = 0 + -0.8 Reorder the terms: 0.8 + -0.8 + -2T + T2 = 0 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + -2T + T2 = 0 + -0.8 -2T + T2 = 0 + -0.8 Combine like terms: 0 + -0.8 = -0.8 -2T + T2 = -0.8 The T term is -2T. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2T + 1 + T2 = -0.8 + 1 Reorder the terms: 1 + -2T + T2 = -0.8 + 1 Combine like terms: -0.8 + 1 = 0.2 1 + -2T + T2 = 0.2 Factor a perfect square on the left side: (T + -1)(T + -1) = 0.2 Calculate the square root of the right side: 0.447213596 Break this problem into two subproblems by setting (T + -1) equal to 0.447213596 and -0.447213596.Subproblem 1
T + -1 = 0.447213596 Simplifying T + -1 = 0.447213596 Reorder the terms: -1 + T = 0.447213596 Solving -1 + T = 0.447213596 Solving for variable 'T'. Move all terms containing T to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + T = 0.447213596 + 1 Combine like terms: -1 + 1 = 0 0 + T = 0.447213596 + 1 T = 0.447213596 + 1 Combine like terms: 0.447213596 + 1 = 1.447213596 T = 1.447213596 Simplifying T = 1.447213596Subproblem 2
T + -1 = -0.447213596 Simplifying T + -1 = -0.447213596 Reorder the terms: -1 + T = -0.447213596 Solving -1 + T = -0.447213596 Solving for variable 'T'. Move all terms containing T to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + T = -0.447213596 + 1 Combine like terms: -1 + 1 = 0 0 + T = -0.447213596 + 1 T = -0.447213596 + 1 Combine like terms: -0.447213596 + 1 = 0.552786404 T = 0.552786404 Simplifying T = 0.552786404Solution
The solution to the problem is based on the solutions from the subproblems. T = {1.447213596, 0.552786404}
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