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Simplifying 0 = 3t2 + -16t + 15 Reorder the terms: 0 = 15 + -16t + 3t2 Solving 0 = 15 + -16t + 3t2 Solving for variable 't'. Combine like terms: 0 + -15 = -15 -15 + 16t + -3t2 = 15 + -16t + 3t2 + -15 + 16t + -3t2 Reorder the terms: -15 + 16t + -3t2 = 15 + -15 + -16t + 16t + 3t2 + -3t2 Combine like terms: 15 + -15 = 0 -15 + 16t + -3t2 = 0 + -16t + 16t + 3t2 + -3t2 -15 + 16t + -3t2 = -16t + 16t + 3t2 + -3t2 Combine like terms: -16t + 16t = 0 -15 + 16t + -3t2 = 0 + 3t2 + -3t2 -15 + 16t + -3t2 = 3t2 + -3t2 Combine like terms: 3t2 + -3t2 = 0 -15 + 16t + -3t2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 5 + -5.333333333t + t2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + -5.333333333t + -5 + t2 = 0 + -5 Reorder the terms: 5 + -5 + -5.333333333t + t2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -5.333333333t + t2 = 0 + -5 -5.333333333t + t2 = 0 + -5 Combine like terms: 0 + -5 = -5 -5.333333333t + t2 = -5 The t term is -5.333333333t. Take half its coefficient (-2.666666667). Square it (7.111111113) and add it to both sides. Add '7.111111113' to each side of the equation. -5.333333333t + 7.111111113 + t2 = -5 + 7.111111113 Reorder the terms: 7.111111113 + -5.333333333t + t2 = -5 + 7.111111113 Combine like terms: -5 + 7.111111113 = 2.111111113 7.111111113 + -5.333333333t + t2 = 2.111111113 Factor a perfect square on the left side: (t + -2.666666667)(t + -2.666666667) = 2.111111113 Calculate the square root of the right side: 1.452966315 Break this problem into two subproblems by setting (t + -2.666666667) equal to 1.452966315 and -1.452966315.Subproblem 1
t + -2.666666667 = 1.452966315 Simplifying t + -2.666666667 = 1.452966315 Reorder the terms: -2.666666667 + t = 1.452966315 Solving -2.666666667 + t = 1.452966315 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.666666667' to each side of the equation. -2.666666667 + 2.666666667 + t = 1.452966315 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + t = 1.452966315 + 2.666666667 t = 1.452966315 + 2.666666667 Combine like terms: 1.452966315 + 2.666666667 = 4.119632982 t = 4.119632982 Simplifying t = 4.119632982Subproblem 2
t + -2.666666667 = -1.452966315 Simplifying t + -2.666666667 = -1.452966315 Reorder the terms: -2.666666667 + t = -1.452966315 Solving -2.666666667 + t = -1.452966315 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.666666667' to each side of the equation. -2.666666667 + 2.666666667 + t = -1.452966315 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + t = -1.452966315 + 2.666666667 t = -1.452966315 + 2.666666667 Combine like terms: -1.452966315 + 2.666666667 = 1.213700352 t = 1.213700352 Simplifying t = 1.213700352Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.119632982, 1.213700352}
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