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Simplifying t = -16t2 + 130t + 2 Reorder the terms: t = 2 + 130t + -16t2 Solving t = 2 + 130t + -16t2 Solving for variable 't'. Reorder the terms: -2 + t + -130t + 16t2 = 2 + 130t + -16t2 + -2 + -130t + 16t2 Combine like terms: t + -130t = -129t -2 + -129t + 16t2 = 2 + 130t + -16t2 + -2 + -130t + 16t2 Reorder the terms: -2 + -129t + 16t2 = 2 + -2 + 130t + -130t + -16t2 + 16t2 Combine like terms: 2 + -2 = 0 -2 + -129t + 16t2 = 0 + 130t + -130t + -16t2 + 16t2 -2 + -129t + 16t2 = 130t + -130t + -16t2 + 16t2 Combine like terms: 130t + -130t = 0 -2 + -129t + 16t2 = 0 + -16t2 + 16t2 -2 + -129t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -2 + -129t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.125 + -8.0625t + t2 = 0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + -8.0625t + 0.125 + t2 = 0 + 0.125 Reorder the terms: -0.125 + 0.125 + -8.0625t + t2 = 0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + -8.0625t + t2 = 0 + 0.125 -8.0625t + t2 = 0 + 0.125 Combine like terms: 0 + 0.125 = 0.125 -8.0625t + t2 = 0.125 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 = 0.125 + 16.25097656 Reorder the terms: 16.25097656 + -8.0625t + t2 = 0.125 + 16.25097656 Combine like terms: 0.125 + 16.25097656 = 16.37597656 16.25097656 + -8.0625t + t2 = 16.37597656 Factor a perfect square on the left side: (t + -4.03125)(t + -4.03125) = 16.37597656 Calculate the square root of the right side: 4.046724176 Break this problem into two subproblems by setting (t + -4.03125) equal to 4.046724176 and -4.046724176.Subproblem 1
t + -4.03125 = 4.046724176 Simplifying t + -4.03125 = 4.046724176 Reorder the terms: -4.03125 + t = 4.046724176 Solving -4.03125 + t = 4.046724176 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 = 4.046724176 + 4.03125 Combine like terms: -4.03125 + 4.03125 = 0.00000 0.00000 + t = 4.046724176 + 4.03125 t = 4.046724176 + 4.03125 Combine like terms: 4.046724176 + 4.03125 = 8.077974176 t = 8.077974176 Simplifying t = 8.077974176Subproblem 2
t + -4.03125 = -4.046724176 Simplifying t + -4.03125 = -4.046724176 Reorder the terms: -4.03125 + t = -4.046724176 Solving -4.03125 + t = -4.046724176 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 = -4.046724176 + 4.03125 Combine like terms: -4.03125 + 4.03125 = 0.00000 0.00000 + t = -4.046724176 + 4.03125 t = -4.046724176 + 4.03125 Combine like terms: -4.046724176 + 4.03125 = -0.015474176 t = -0.015474176 Simplifying t = -0.015474176Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.077974176, -0.015474176}
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