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Simplifying 4.90t2 = (2.40 + -1t) * 336 Reorder the terms for easier multiplication: 4.90t2 = 336(2.40 + -1t) 4.90t2 = (2.40 * 336 + -1t * 336) 4.90t2 = (806.4 + -336t) Solving 4.90t2 = 806.4 + -336t Solving for variable 't'. Reorder the terms: -806.4 + 336t + 4.90t2 = 806.4 + -336t + -806.4 + 336t Reorder the terms: -806.4 + 336t + 4.90t2 = 806.4 + -806.4 + -336t + 336t Combine like terms: 806.4 + -806.4 = 0.0 -806.4 + 336t + 4.90t2 = 0.0 + -336t + 336t -806.4 + 336t + 4.90t2 = -336t + 336t Combine like terms: -336t + 336t = 0 -806.4 + 336t + 4.90t2 = 0 Begin completing the square. Divide all terms by 4.90 the coefficient of the squared term: Divide each side by '4.90'. -164.5714286 + 68.57142857t + t2 = 0 Move the constant term to the right: Add '164.5714286' to each side of the equation. -164.5714286 + 68.57142857t + 164.5714286 + t2 = 0 + 164.5714286 Reorder the terms: -164.5714286 + 164.5714286 + 68.57142857t + t2 = 0 + 164.5714286 Combine like terms: -164.5714286 + 164.5714286 = 0.0000000 0.0000000 + 68.57142857t + t2 = 0 + 164.5714286 68.57142857t + t2 = 0 + 164.5714286 Combine like terms: 0 + 164.5714286 = 164.5714286 68.57142857t + t2 = 164.5714286 The t term is 68.57142857t. Take half its coefficient (34.28571429). Square it (1175.510204) and add it to both sides. Add '1175.510204' to each side of the equation. 68.57142857t + 1175.510204 + t2 = 164.5714286 + 1175.510204 Reorder the terms: 1175.510204 + 68.57142857t + t2 = 164.5714286 + 1175.510204 Combine like terms: 164.5714286 + 1175.510204 = 1340.0816326 1175.510204 + 68.57142857t + t2 = 1340.0816326 Factor a perfect square on the left side: (t + 34.28571429)(t + 34.28571429) = 1340.0816326 Calculate the square root of the right side: 36.607125435 Break this problem into two subproblems by setting (t + 34.28571429) equal to 36.607125435 and -36.607125435.Subproblem 1
t + 34.28571429 = 36.607125435 Simplifying t + 34.28571429 = 36.607125435 Reorder the terms: 34.28571429 + t = 36.607125435 Solving 34.28571429 + t = 36.607125435 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-34.28571429' to each side of the equation. 34.28571429 + -34.28571429 + t = 36.607125435 + -34.28571429 Combine like terms: 34.28571429 + -34.28571429 = 0.00000000 0.00000000 + t = 36.607125435 + -34.28571429 t = 36.607125435 + -34.28571429 Combine like terms: 36.607125435 + -34.28571429 = 2.321411145 t = 2.321411145 Simplifying t = 2.321411145Subproblem 2
t + 34.28571429 = -36.607125435 Simplifying t + 34.28571429 = -36.607125435 Reorder the terms: 34.28571429 + t = -36.607125435 Solving 34.28571429 + t = -36.607125435 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-34.28571429' to each side of the equation. 34.28571429 + -34.28571429 + t = -36.607125435 + -34.28571429 Combine like terms: 34.28571429 + -34.28571429 = 0.00000000 0.00000000 + t = -36.607125435 + -34.28571429 t = -36.607125435 + -34.28571429 Combine like terms: -36.607125435 + -34.28571429 = -70.892839725 t = -70.892839725 Simplifying t = -70.892839725Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.321411145, -70.892839725}
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