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Simplifying 4 = -16t2 + 129t Reorder the terms: 4 = 129t + -16t2 Solving 4 = 129t + -16t2 Solving for variable 't'. Reorder the terms: 4 + -129t + 16t2 = 129t + -129t + -16t2 + 16t2 Combine like terms: 129t + -129t = 0 4 + -129t + 16t2 = 0 + -16t2 + 16t2 4 + -129t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 4 + -129t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.25 + -8.0625t + t2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + -8.0625t + -0.25 + t2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + -8.0625t + t2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + -8.0625t + t2 = 0 + -0.25 -8.0625t + t2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 -8.0625t + t2 = -0.25 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 = -0.25 + 16.25097656 Reorder the terms: 16.25097656 + -8.0625t + t2 = -0.25 + 16.25097656 Combine like terms: -0.25 + 16.25097656 = 16.00097656 16.25097656 + -8.0625t + t2 = 16.00097656 Factor a perfect square on the left side: (t + -4.03125)(t + -4.03125) = 16.00097656 Calculate the square root of the right side: 4.000122068 Break this problem into two subproblems by setting (t + -4.03125) equal to 4.000122068 and -4.000122068.Subproblem 1
t + -4.03125 = 4.000122068 Simplifying t + -4.03125 = 4.000122068 Reorder the terms: -4.03125 + t = 4.000122068 Solving -4.03125 + t = 4.000122068 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 = 4.000122068 + 4.03125 Combine like terms: -4.03125 + 4.03125 = 0.00000 0.00000 + t = 4.000122068 + 4.03125 t = 4.000122068 + 4.03125 Combine like terms: 4.000122068 + 4.03125 = 8.031372068 t = 8.031372068 Simplifying t = 8.031372068Subproblem 2
t + -4.03125 = -4.000122068 Simplifying t + -4.03125 = -4.000122068 Reorder the terms: -4.03125 + t = -4.000122068 Solving -4.03125 + t = -4.000122068 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 = -4.000122068 + 4.03125 Combine like terms: -4.03125 + 4.03125 = 0.00000 0.00000 + t = -4.000122068 + 4.03125 t = -4.000122068 + 4.03125 Combine like terms: -4.000122068 + 4.03125 = 0.031127932 t = 0.031127932 Simplifying t = 0.031127932Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.031372068, 0.031127932}
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