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Simplifying 272 = -16t2 + 129t + 42 Reorder the terms: 272 = 42 + 129t + -16t2 Solving 272 = 42 + 129t + -16t2 Solving for variable 't'. Combine like terms: 272 + -42 = 230 230 + -129t + 16t2 = 42 + 129t + -16t2 + -42 + -129t + 16t2 Reorder the terms: 230 + -129t + 16t2 = 42 + -42 + 129t + -129t + -16t2 + 16t2 Combine like terms: 42 + -42 = 0 230 + -129t + 16t2 = 0 + 129t + -129t + -16t2 + 16t2 230 + -129t + 16t2 = 129t + -129t + -16t2 + 16t2 Combine like terms: 129t + -129t = 0 230 + -129t + 16t2 = 0 + -16t2 + 16t2 230 + -129t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 230 + -129t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 14.375 + -8.0625t + t2 = 0 Move the constant term to the right: Add '-14.375' to each side of the equation. 14.375 + -8.0625t + -14.375 + t2 = 0 + -14.375 Reorder the terms: 14.375 + -14.375 + -8.0625t + t2 = 0 + -14.375 Combine like terms: 14.375 + -14.375 = 0.000 0.000 + -8.0625t + t2 = 0 + -14.375 -8.0625t + t2 = 0 + -14.375 Combine like terms: 0 + -14.375 = -14.375 -8.0625t + t2 = -14.375 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 = -14.375 + 16.25097656 Reorder the terms: 16.25097656 + -8.0625t + t2 = -14.375 + 16.25097656 Combine like terms: -14.375 + 16.25097656 = 1.87597656 16.25097656 + -8.0625t + t2 = 1.87597656 Factor a perfect square on the left side: (t + -4.03125)(t + -4.03125) = 1.87597656 Calculate the square root of the right side: 1.369662937 Break this problem into two subproblems by setting (t + -4.03125) equal to 1.369662937 and -1.369662937.Subproblem 1
t + -4.03125 = 1.369662937 Simplifying t + -4.03125 = 1.369662937 Reorder the terms: -4.03125 + t = 1.369662937 Solving -4.03125 + t = 1.369662937 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 = 1.369662937 + 4.03125 Combine like terms: -4.03125 + 4.03125 = 0.00000 0.00000 + t = 1.369662937 + 4.03125 t = 1.369662937 + 4.03125 Combine like terms: 1.369662937 + 4.03125 = 5.400912937 t = 5.400912937 Simplifying t = 5.400912937Subproblem 2
t + -4.03125 = -1.369662937 Simplifying t + -4.03125 = -1.369662937 Reorder the terms: -4.03125 + t = -1.369662937 Solving -4.03125 + t = -1.369662937 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 = -1.369662937 + 4.03125 Combine like terms: -4.03125 + 4.03125 = 0.00000 0.00000 + t = -1.369662937 + 4.03125 t = -1.369662937 + 4.03125 Combine like terms: -1.369662937 + 4.03125 = 2.661587063 t = 2.661587063 Simplifying t = 2.661587063Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.400912937, 2.661587063}
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