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Simplifying 200 = -16t2 + 118t + 3 Reorder the terms: 200 = 3 + 118t + -16t2 Solving 200 = 3 + 118t + -16t2 Solving for variable 't'. Combine like terms: 200 + -3 = 197 197 + -118t + 16t2 = 3 + 118t + -16t2 + -3 + -118t + 16t2 Reorder the terms: 197 + -118t + 16t2 = 3 + -3 + 118t + -118t + -16t2 + 16t2 Combine like terms: 3 + -3 = 0 197 + -118t + 16t2 = 0 + 118t + -118t + -16t2 + 16t2 197 + -118t + 16t2 = 118t + -118t + -16t2 + 16t2 Combine like terms: 118t + -118t = 0 197 + -118t + 16t2 = 0 + -16t2 + 16t2 197 + -118t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 197 + -118t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 12.3125 + -7.375t + t2 = 0 Move the constant term to the right: Add '-12.3125' to each side of the equation. 12.3125 + -7.375t + -12.3125 + t2 = 0 + -12.3125 Reorder the terms: 12.3125 + -12.3125 + -7.375t + t2 = 0 + -12.3125 Combine like terms: 12.3125 + -12.3125 = 0.0000 0.0000 + -7.375t + t2 = 0 + -12.3125 -7.375t + t2 = 0 + -12.3125 Combine like terms: 0 + -12.3125 = -12.3125 -7.375t + t2 = -12.3125 The t term is -7.375t. Take half its coefficient (-3.6875). Square it (13.59765625) and add it to both sides. Add '13.59765625' to each side of the equation. -7.375t + 13.59765625 + t2 = -12.3125 + 13.59765625 Reorder the terms: 13.59765625 + -7.375t + t2 = -12.3125 + 13.59765625 Combine like terms: -12.3125 + 13.59765625 = 1.28515625 13.59765625 + -7.375t + t2 = 1.28515625 Factor a perfect square on the left side: (t + -3.6875)(t + -3.6875) = 1.28515625 Calculate the square root of the right side: 1.133647322 Break this problem into two subproblems by setting (t + -3.6875) equal to 1.133647322 and -1.133647322.Subproblem 1
t + -3.6875 = 1.133647322 Simplifying t + -3.6875 = 1.133647322 Reorder the terms: -3.6875 + t = 1.133647322 Solving -3.6875 + t = 1.133647322 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.6875' to each side of the equation. -3.6875 + 3.6875 + t = 1.133647322 + 3.6875 Combine like terms: -3.6875 + 3.6875 = 0.0000 0.0000 + t = 1.133647322 + 3.6875 t = 1.133647322 + 3.6875 Combine like terms: 1.133647322 + 3.6875 = 4.821147322 t = 4.821147322 Simplifying t = 4.821147322Subproblem 2
t + -3.6875 = -1.133647322 Simplifying t + -3.6875 = -1.133647322 Reorder the terms: -3.6875 + t = -1.133647322 Solving -3.6875 + t = -1.133647322 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.6875' to each side of the equation. -3.6875 + 3.6875 + t = -1.133647322 + 3.6875 Combine like terms: -3.6875 + 3.6875 = 0.0000 0.0000 + t = -1.133647322 + 3.6875 t = -1.133647322 + 3.6875 Combine like terms: -1.133647322 + 3.6875 = 2.553852678 t = 2.553852678 Simplifying t = 2.553852678Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.821147322, 2.553852678}
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