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Simplifying 3t2 = t + 6 Reorder the terms: 3t2 = 6 + t Solving 3t2 = 6 + t Solving for variable 't'. Reorder the terms: -6 + -1t + 3t2 = 6 + t + -6 + -1t Reorder the terms: -6 + -1t + 3t2 = 6 + -6 + t + -1t Combine like terms: 6 + -6 = 0 -6 + -1t + 3t2 = 0 + t + -1t -6 + -1t + 3t2 = t + -1t Combine like terms: t + -1t = 0 -6 + -1t + 3t2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2 + -0.3333333333t + t2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -0.3333333333t + 2 + t2 = 0 + 2 Reorder the terms: -2 + 2 + -0.3333333333t + t2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -0.3333333333t + t2 = 0 + 2 -0.3333333333t + t2 = 0 + 2 Combine like terms: 0 + 2 = 2 -0.3333333333t + t2 = 2 The t term is -0.3333333333t. Take half its coefficient (-0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. -0.3333333333t + 0.02777777779 + t2 = 2 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333t + t2 = 2 + 0.02777777779 Combine like terms: 2 + 0.02777777779 = 2.02777777779 0.02777777779 + -0.3333333333t + t2 = 2.02777777779 Factor a perfect square on the left side: (t + -0.1666666667)(t + -0.1666666667) = 2.02777777779 Calculate the square root of the right side: 1.424000624 Break this problem into two subproblems by setting (t + -0.1666666667) equal to 1.424000624 and -1.424000624.Subproblem 1
t + -0.1666666667 = 1.424000624 Simplifying t + -0.1666666667 = 1.424000624 Reorder the terms: -0.1666666667 + t = 1.424000624 Solving -0.1666666667 + t = 1.424000624 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + t = 1.424000624 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + t = 1.424000624 + 0.1666666667 t = 1.424000624 + 0.1666666667 Combine like terms: 1.424000624 + 0.1666666667 = 1.5906672907 t = 1.5906672907 Simplifying t = 1.5906672907Subproblem 2
t + -0.1666666667 = -1.424000624 Simplifying t + -0.1666666667 = -1.424000624 Reorder the terms: -0.1666666667 + t = -1.424000624 Solving -0.1666666667 + t = -1.424000624 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + t = -1.424000624 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + t = -1.424000624 + 0.1666666667 t = -1.424000624 + 0.1666666667 Combine like terms: -1.424000624 + 0.1666666667 = -1.2573339573 t = -1.2573339573 Simplifying t = -1.2573339573Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.5906672907, -1.2573339573}
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