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Simplifying 3t2 + 6t + -1 = 0 Reorder the terms: -1 + 6t + 3t2 = 0 Solving -1 + 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'. -0.3333333333 + 2t + t2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + 2t + 0.3333333333 + t2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + 2t + t2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + 2t + t2 = 0 + 0.3333333333 2t + t2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 2t + t2 = 0.3333333333 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 = 0.3333333333 + 1 Reorder the terms: 1 + 2t + t2 = 0.3333333333 + 1 Combine like terms: 0.3333333333 + 1 = 1.3333333333 1 + 2t + t2 = 1.3333333333 Factor a perfect square on the left side: (t + 1)(t + 1) = 1.3333333333 Calculate the square root of the right side: 1.154700538 Break this problem into two subproblems by setting (t + 1) equal to 1.154700538 and -1.154700538.Subproblem 1
t + 1 = 1.154700538 Simplifying t + 1 = 1.154700538 Reorder the terms: 1 + t = 1.154700538 Solving 1 + t = 1.154700538 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 = 1.154700538 + -1 Combine like terms: 1 + -1 = 0 0 + t = 1.154700538 + -1 t = 1.154700538 + -1 Combine like terms: 1.154700538 + -1 = 0.154700538 t = 0.154700538 Simplifying t = 0.154700538Subproblem 2
t + 1 = -1.154700538 Simplifying t + 1 = -1.154700538 Reorder the terms: 1 + t = -1.154700538 Solving 1 + t = -1.154700538 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 = -1.154700538 + -1 Combine like terms: 1 + -1 = 0 0 + t = -1.154700538 + -1 t = -1.154700538 + -1 Combine like terms: -1.154700538 + -1 = -2.154700538 t = -2.154700538 Simplifying t = -2.154700538Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.154700538, -2.154700538}
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