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Simplifying -16t2 + 129t + -5 = 0 Reorder the terms: -5 + 129t + -16t2 = 0 Solving -5 + 129t + -16t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. 0.3125 + -8.0625t + t2 = 0 Move the constant term to the right: Add '-0.3125' to each side of the equation. 0.3125 + -8.0625t + -0.3125 + t2 = 0 + -0.3125 Reorder the terms: 0.3125 + -0.3125 + -8.0625t + t2 = 0 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + -8.0625t + t2 = 0 + -0.3125 -8.0625t + t2 = 0 + -0.3125 Combine like terms: 0 + -0.3125 = -0.3125 -8.0625t + t2 = -0.3125 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 = -0.3125 + 16.25097656 Reorder the terms: 16.25097656 + -8.0625t + t2 = -0.3125 + 16.25097656 Combine like terms: -0.3125 + 16.25097656 = 15.93847656 16.25097656 + -8.0625t + t2 = 15.93847656 Factor a perfect square on the left side: (t + -4.03125)(t + -4.03125) = 15.93847656 Calculate the square root of the right side: 3.992302163 Break this problem into two subproblems by setting (t + -4.03125) equal to 3.992302163 and -3.992302163.Subproblem 1
t + -4.03125 = 3.992302163 Simplifying t + -4.03125 = 3.992302163 Reorder the terms: -4.03125 + t = 3.992302163 Solving -4.03125 + t = 3.992302163 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 = 3.992302163 + 4.03125 Combine like terms: -4.03125 + 4.03125 = 0.00000 0.00000 + t = 3.992302163 + 4.03125 t = 3.992302163 + 4.03125 Combine like terms: 3.992302163 + 4.03125 = 8.023552163 t = 8.023552163 Simplifying t = 8.023552163Subproblem 2
t + -4.03125 = -3.992302163 Simplifying t + -4.03125 = -3.992302163 Reorder the terms: -4.03125 + t = -3.992302163 Solving -4.03125 + t = -3.992302163 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 = -3.992302163 + 4.03125 Combine like terms: -4.03125 + 4.03125 = 0.00000 0.00000 + t = -3.992302163 + 4.03125 t = -3.992302163 + 4.03125 Combine like terms: -3.992302163 + 4.03125 = 0.038947837 t = 0.038947837 Simplifying t = 0.038947837Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.023552163, 0.038947837}
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