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Simplifying -24 = -11.6t + -4.9t2 Solving -24 = -11.6t + -4.9t2 Solving for variable 't'. Reorder the terms: -24 + 11.6t + 4.9t2 = -11.6t + 11.6t + -4.9t2 + 4.9t2 Combine like terms: -11.6t + 11.6t = 0.0 -24 + 11.6t + 4.9t2 = 0.0 + -4.9t2 + 4.9t2 -24 + 11.6t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -24 + 11.6t + 4.9t2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -4.897959184 + 2.367346939t + t2 = 0 Move the constant term to the right: Add '4.897959184' to each side of the equation. -4.897959184 + 2.367346939t + 4.897959184 + t2 = 0 + 4.897959184 Reorder the terms: -4.897959184 + 4.897959184 + 2.367346939t + t2 = 0 + 4.897959184 Combine like terms: -4.897959184 + 4.897959184 = 0.000000000 0.000000000 + 2.367346939t + t2 = 0 + 4.897959184 2.367346939t + t2 = 0 + 4.897959184 Combine like terms: 0 + 4.897959184 = 4.897959184 2.367346939t + t2 = 4.897959184 The t term is 2.367346939t. Take half its coefficient (1.18367347). Square it (1.401082884) and add it to both sides. Add '1.401082884' to each side of the equation. 2.367346939t + 1.401082884 + t2 = 4.897959184 + 1.401082884 Reorder the terms: 1.401082884 + 2.367346939t + t2 = 4.897959184 + 1.401082884 Combine like terms: 4.897959184 + 1.401082884 = 6.299042068 1.401082884 + 2.367346939t + t2 = 6.299042068 Factor a perfect square on the left side: (t + 1.18367347)(t + 1.18367347) = 6.299042068 Calculate the square root of the right side: 2.509789248 Break this problem into two subproblems by setting (t + 1.18367347) equal to 2.509789248 and -2.509789248.Subproblem 1
t + 1.18367347 = 2.509789248 Simplifying t + 1.18367347 = 2.509789248 Reorder the terms: 1.18367347 + t = 2.509789248 Solving 1.18367347 + t = 2.509789248 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.18367347' to each side of the equation. 1.18367347 + -1.18367347 + t = 2.509789248 + -1.18367347 Combine like terms: 1.18367347 + -1.18367347 = 0.00000000 0.00000000 + t = 2.509789248 + -1.18367347 t = 2.509789248 + -1.18367347 Combine like terms: 2.509789248 + -1.18367347 = 1.326115778 t = 1.326115778 Simplifying t = 1.326115778Subproblem 2
t + 1.18367347 = -2.509789248 Simplifying t + 1.18367347 = -2.509789248 Reorder the terms: 1.18367347 + t = -2.509789248 Solving 1.18367347 + t = -2.509789248 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.18367347' to each side of the equation. 1.18367347 + -1.18367347 + t = -2.509789248 + -1.18367347 Combine like terms: 1.18367347 + -1.18367347 = 0.00000000 0.00000000 + t = -2.509789248 + -1.18367347 t = -2.509789248 + -1.18367347 Combine like terms: -2.509789248 + -1.18367347 = -3.693462718 t = -3.693462718 Simplifying t = -3.693462718Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.326115778, -3.693462718}
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