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Simplifying 4.9t2 + 2t + -1 = 0 Reorder the terms: -1 + 2t + 4.9t2 = 0 Solving -1 + 2t + 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'. -0.2040816327 + 0.4081632653t + t2 = 0 Move the constant term to the right: Add '0.2040816327' to each side of the equation. -0.2040816327 + 0.4081632653t + 0.2040816327 + t2 = 0 + 0.2040816327 Reorder the terms: -0.2040816327 + 0.2040816327 + 0.4081632653t + t2 = 0 + 0.2040816327 Combine like terms: -0.2040816327 + 0.2040816327 = 0.0000000000 0.0000000000 + 0.4081632653t + t2 = 0 + 0.2040816327 0.4081632653t + t2 = 0 + 0.2040816327 Combine like terms: 0 + 0.2040816327 = 0.2040816327 0.4081632653t + t2 = 0.2040816327 The t term is 0.4081632653t. Take half its coefficient (0.2040816327). Square it (0.04164931281) and add it to both sides. Add '0.04164931281' to each side of the equation. 0.4081632653t + 0.04164931281 + t2 = 0.2040816327 + 0.04164931281 Reorder the terms: 0.04164931281 + 0.4081632653t + t2 = 0.2040816327 + 0.04164931281 Combine like terms: 0.2040816327 + 0.04164931281 = 0.24573094551 0.04164931281 + 0.4081632653t + t2 = 0.24573094551 Factor a perfect square on the left side: (t + 0.2040816327)(t + 0.2040816327) = 0.24573094551 Calculate the square root of the right side: 0.495712563 Break this problem into two subproblems by setting (t + 0.2040816327) equal to 0.495712563 and -0.495712563.Subproblem 1
t + 0.2040816327 = 0.495712563 Simplifying t + 0.2040816327 = 0.495712563 Reorder the terms: 0.2040816327 + t = 0.495712563 Solving 0.2040816327 + t = 0.495712563 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.2040816327' to each side of the equation. 0.2040816327 + -0.2040816327 + t = 0.495712563 + -0.2040816327 Combine like terms: 0.2040816327 + -0.2040816327 = 0.0000000000 0.0000000000 + t = 0.495712563 + -0.2040816327 t = 0.495712563 + -0.2040816327 Combine like terms: 0.495712563 + -0.2040816327 = 0.2916309303 t = 0.2916309303 Simplifying t = 0.2916309303Subproblem 2
t + 0.2040816327 = -0.495712563 Simplifying t + 0.2040816327 = -0.495712563 Reorder the terms: 0.2040816327 + t = -0.495712563 Solving 0.2040816327 + t = -0.495712563 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.2040816327' to each side of the equation. 0.2040816327 + -0.2040816327 + t = -0.495712563 + -0.2040816327 Combine like terms: 0.2040816327 + -0.2040816327 = 0.0000000000 0.0000000000 + t = -0.495712563 + -0.2040816327 t = -0.495712563 + -0.2040816327 Combine like terms: -0.495712563 + -0.2040816327 = -0.6997941957 t = -0.6997941957 Simplifying t = -0.6997941957Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.2916309303, -0.6997941957}
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