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Simplifying 129 = -16t2 + 129t Reorder the terms: 129 = 129t + -16t2 Solving 129 = 129t + -16t2 Solving for variable 't'. Reorder the terms: 129 + -129t + 16t2 = 129t + -129t + -16t2 + 16t2 Combine like terms: 129t + -129t = 0 129 + -129t + 16t2 = 0 + -16t2 + 16t2 129 + -129t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 129 + -129t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 8.0625 + -8.0625t + t2 = 0 Move the constant term to the right: Add '-8.0625' to each side of the equation. 8.0625 + -8.0625t + -8.0625 + t2 = 0 + -8.0625 Reorder the terms: 8.0625 + -8.0625 + -8.0625t + t2 = 0 + -8.0625 Combine like terms: 8.0625 + -8.0625 = 0.0000 0.0000 + -8.0625t + t2 = 0 + -8.0625 -8.0625t + t2 = 0 + -8.0625 Combine like terms: 0 + -8.0625 = -8.0625 -8.0625t + t2 = -8.0625 The t term is -8.0625t. Take half its coefficient (-4.03125). Square it (16.25097656) and add it to both sides. Add '16.25097656' to each side of the equation. -8.0625t + 16.25097656 + t2 = -8.0625 + 16.25097656 Reorder the terms: 16.25097656 + -8.0625t + t2 = -8.0625 + 16.25097656 Combine like terms: -8.0625 + 16.25097656 = 8.18847656 16.25097656 + -8.0625t + t2 = 8.18847656 Factor a perfect square on the left side: (t + -4.03125)(t + -4.03125) = 8.18847656 Calculate the square root of the right side: 2.861551425 Break this problem into two subproblems by setting (t + -4.03125) equal to 2.861551425 and -2.861551425.Subproblem 1
t + -4.03125 = 2.861551425 Simplifying t + -4.03125 = 2.861551425 Reorder the terms: -4.03125 + t = 2.861551425 Solving -4.03125 + t = 2.861551425 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.03125' to each side of the equation. -4.03125 + 4.03125 + t = 2.861551425 + 4.03125 Combine like terms: -4.03125 + 4.03125 = 0.00000 0.00000 + t = 2.861551425 + 4.03125 t = 2.861551425 + 4.03125 Combine like terms: 2.861551425 + 4.03125 = 6.892801425 t = 6.892801425 Simplifying t = 6.892801425Subproblem 2
t + -4.03125 = -2.861551425 Simplifying t + -4.03125 = -2.861551425 Reorder the terms: -4.03125 + t = -2.861551425 Solving -4.03125 + t = -2.861551425 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.03125' to each side of the equation. -4.03125 + 4.03125 + t = -2.861551425 + 4.03125 Combine like terms: -4.03125 + 4.03125 = 0.00000 0.00000 + t = -2.861551425 + 4.03125 t = -2.861551425 + 4.03125 Combine like terms: -2.861551425 + 4.03125 = 1.169698575 t = 1.169698575 Simplifying t = 1.169698575Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.892801425, 1.169698575}
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