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Simplifying 4.9t2 + 1.6t + -1.06 = 0 Reorder the terms: -1.06 + 1.6t + 4.9t2 = 0 Solving -1.06 + 1.6t + 4.9t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -0.2163265306 + 0.3265306122t + t2 = 0 Move the constant term to the right: Add '0.2163265306' to each side of the equation. -0.2163265306 + 0.3265306122t + 0.2163265306 + t2 = 0 + 0.2163265306 Reorder the terms: -0.2163265306 + 0.2163265306 + 0.3265306122t + t2 = 0 + 0.2163265306 Combine like terms: -0.2163265306 + 0.2163265306 = 0.0000000000 0.0000000000 + 0.3265306122t + t2 = 0 + 0.2163265306 0.3265306122t + t2 = 0 + 0.2163265306 Combine like terms: 0 + 0.2163265306 = 0.2163265306 0.3265306122t + t2 = 0.2163265306 The t term is 0.3265306122t. Take half its coefficient (0.1632653061). Square it (0.02665556018) and add it to both sides. Add '0.02665556018' to each side of the equation. 0.3265306122t + 0.02665556018 + t2 = 0.2163265306 + 0.02665556018 Reorder the terms: 0.02665556018 + 0.3265306122t + t2 = 0.2163265306 + 0.02665556018 Combine like terms: 0.2163265306 + 0.02665556018 = 0.24298209078 0.02665556018 + 0.3265306122t + t2 = 0.24298209078 Factor a perfect square on the left side: (t + 0.1632653061)(t + 0.1632653061) = 0.24298209078 Calculate the square root of the right side: 0.492932136 Break this problem into two subproblems by setting (t + 0.1632653061) equal to 0.492932136 and -0.492932136.Subproblem 1
t + 0.1632653061 = 0.492932136 Simplifying t + 0.1632653061 = 0.492932136 Reorder the terms: 0.1632653061 + t = 0.492932136 Solving 0.1632653061 + t = 0.492932136 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.1632653061' to each side of the equation. 0.1632653061 + -0.1632653061 + t = 0.492932136 + -0.1632653061 Combine like terms: 0.1632653061 + -0.1632653061 = 0.0000000000 0.0000000000 + t = 0.492932136 + -0.1632653061 t = 0.492932136 + -0.1632653061 Combine like terms: 0.492932136 + -0.1632653061 = 0.3296668299 t = 0.3296668299 Simplifying t = 0.3296668299Subproblem 2
t + 0.1632653061 = -0.492932136 Simplifying t + 0.1632653061 = -0.492932136 Reorder the terms: 0.1632653061 + t = -0.492932136 Solving 0.1632653061 + t = -0.492932136 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.1632653061' to each side of the equation. 0.1632653061 + -0.1632653061 + t = -0.492932136 + -0.1632653061 Combine like terms: 0.1632653061 + -0.1632653061 = 0.0000000000 0.0000000000 + t = -0.492932136 + -0.1632653061 t = -0.492932136 + -0.1632653061 Combine like terms: -0.492932136 + -0.1632653061 = -0.6561974421 t = -0.6561974421 Simplifying t = -0.6561974421Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.3296668299, -0.6561974421}
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