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Simplifying 0 = -4.9t2 + 16t + 5 Reorder the terms: 0 = 5 + 16t + -4.9t2 Solving 0 = 5 + 16t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -5 = -5 -5 + -16t + 4.9t2 = 5 + 16t + -4.9t2 + -5 + -16t + 4.9t2 Reorder the terms: -5 + -16t + 4.9t2 = 5 + -5 + 16t + -16t + -4.9t2 + 4.9t2 Combine like terms: 5 + -5 = 0 -5 + -16t + 4.9t2 = 0 + 16t + -16t + -4.9t2 + 4.9t2 -5 + -16t + 4.9t2 = 16t + -16t + -4.9t2 + 4.9t2 Combine like terms: 16t + -16t = 0 -5 + -16t + 4.9t2 = 0 + -4.9t2 + 4.9t2 -5 + -16t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -5 + -16t + 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'. -1.020408163 + -3.265306122t + t2 = 0 Move the constant term to the right: Add '1.020408163' to each side of the equation. -1.020408163 + -3.265306122t + 1.020408163 + t2 = 0 + 1.020408163 Reorder the terms: -1.020408163 + 1.020408163 + -3.265306122t + t2 = 0 + 1.020408163 Combine like terms: -1.020408163 + 1.020408163 = 0.000000000 0.000000000 + -3.265306122t + t2 = 0 + 1.020408163 -3.265306122t + t2 = 0 + 1.020408163 Combine like terms: 0 + 1.020408163 = 1.020408163 -3.265306122t + t2 = 1.020408163 The t term is -3.265306122t. Take half its coefficient (-1.632653061). Square it (2.665556018) and add it to both sides. Add '2.665556018' to each side of the equation. -3.265306122t + 2.665556018 + t2 = 1.020408163 + 2.665556018 Reorder the terms: 2.665556018 + -3.265306122t + t2 = 1.020408163 + 2.665556018 Combine like terms: 1.020408163 + 2.665556018 = 3.685964181 2.665556018 + -3.265306122t + t2 = 3.685964181 Factor a perfect square on the left side: (t + -1.632653061)(t + -1.632653061) = 3.685964181 Calculate the square root of the right side: 1.919886502 Break this problem into two subproblems by setting (t + -1.632653061) equal to 1.919886502 and -1.919886502.Subproblem 1
t + -1.632653061 = 1.919886502 Simplifying t + -1.632653061 = 1.919886502 Reorder the terms: -1.632653061 + t = 1.919886502 Solving -1.632653061 + t = 1.919886502 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.632653061' to each side of the equation. -1.632653061 + 1.632653061 + t = 1.919886502 + 1.632653061 Combine like terms: -1.632653061 + 1.632653061 = 0.000000000 0.000000000 + t = 1.919886502 + 1.632653061 t = 1.919886502 + 1.632653061 Combine like terms: 1.919886502 + 1.632653061 = 3.552539563 t = 3.552539563 Simplifying t = 3.552539563Subproblem 2
t + -1.632653061 = -1.919886502 Simplifying t + -1.632653061 = -1.919886502 Reorder the terms: -1.632653061 + t = -1.919886502 Solving -1.632653061 + t = -1.919886502 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.632653061' to each side of the equation. -1.632653061 + 1.632653061 + t = -1.919886502 + 1.632653061 Combine like terms: -1.632653061 + 1.632653061 = 0.000000000 0.000000000 + t = -1.919886502 + 1.632653061 t = -1.919886502 + 1.632653061 Combine like terms: -1.919886502 + 1.632653061 = -0.287233441 t = -0.287233441 Simplifying t = -0.287233441Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.552539563, -0.287233441}
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