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Simplifying 3T2 + 6T + -2 = 0 Reorder the terms: -2 + 6T + 3T2 = 0 Solving -2 + 6T + 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'. -0.6666666667 + 2T + T2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + 2T + 0.6666666667 + T2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + 2T + T2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + 2T + T2 = 0 + 0.6666666667 2T + T2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 2T + T2 = 0.6666666667 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 = 0.6666666667 + 1 Reorder the terms: 1 + 2T + T2 = 0.6666666667 + 1 Combine like terms: 0.6666666667 + 1 = 1.6666666667 1 + 2T + T2 = 1.6666666667 Factor a perfect square on the left side: (T + 1)(T + 1) = 1.6666666667 Calculate the square root of the right side: 1.290994449 Break this problem into two subproblems by setting (T + 1) equal to 1.290994449 and -1.290994449.Subproblem 1
T + 1 = 1.290994449 Simplifying T + 1 = 1.290994449 Reorder the terms: 1 + T = 1.290994449 Solving 1 + T = 1.290994449 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 = 1.290994449 + -1 Combine like terms: 1 + -1 = 0 0 + T = 1.290994449 + -1 T = 1.290994449 + -1 Combine like terms: 1.290994449 + -1 = 0.290994449 T = 0.290994449 Simplifying T = 0.290994449Subproblem 2
T + 1 = -1.290994449 Simplifying T + 1 = -1.290994449 Reorder the terms: 1 + T = -1.290994449 Solving 1 + T = -1.290994449 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 = -1.290994449 + -1 Combine like terms: 1 + -1 = 0 0 + T = -1.290994449 + -1 T = -1.290994449 + -1 Combine like terms: -1.290994449 + -1 = -2.290994449 T = -2.290994449 Simplifying T = -2.290994449Solution
The solution to the problem is based on the solutions from the subproblems. T = {0.290994449, -2.290994449}
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