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Simplifying 0.204 = 2t + -4.9t2 Solving 0.204 = 2t + -4.9t2 Solving for variable 't'. Reorder the terms: 0.204 + -2t + 4.9t2 = 2t + -2t + -4.9t2 + 4.9t2 Combine like terms: 2t + -2t = 0 0.204 + -2t + 4.9t2 = 0 + -4.9t2 + 4.9t2 0.204 + -2t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 0.204 + -2t + 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'. 0.04163265306 + -0.4081632653t + t2 = 0 Move the constant term to the right: Add '-0.04163265306' to each side of the equation. 0.04163265306 + -0.4081632653t + -0.04163265306 + t2 = 0 + -0.04163265306 Reorder the terms: 0.04163265306 + -0.04163265306 + -0.4081632653t + t2 = 0 + -0.04163265306 Combine like terms: 0.04163265306 + -0.04163265306 = 0.00000000000 0.00000000000 + -0.4081632653t + t2 = 0 + -0.04163265306 -0.4081632653t + t2 = 0 + -0.04163265306 Combine like terms: 0 + -0.04163265306 = -0.04163265306 -0.4081632653t + t2 = -0.04163265306 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 = -0.04163265306 + 0.04164931281 Reorder the terms: 0.04164931281 + -0.4081632653t + t2 = -0.04163265306 + 0.04164931281 Combine like terms: -0.04163265306 + 0.04164931281 = 0.00001665975 0.04164931281 + -0.4081632653t + t2 = 0.00001665975 Factor a perfect square on the left side: (t + -0.2040816327)(t + -0.2040816327) = 0.00001665975 Calculate the square root of the right side: 0.004081636 Break this problem into two subproblems by setting (t + -0.2040816327) equal to 0.004081636 and -0.004081636.Subproblem 1
t + -0.2040816327 = 0.004081636 Simplifying t + -0.2040816327 = 0.004081636 Reorder the terms: -0.2040816327 + t = 0.004081636 Solving -0.2040816327 + t = 0.004081636 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 = 0.004081636 + 0.2040816327 Combine like terms: -0.2040816327 + 0.2040816327 = 0.0000000000 0.0000000000 + t = 0.004081636 + 0.2040816327 t = 0.004081636 + 0.2040816327 Combine like terms: 0.004081636 + 0.2040816327 = 0.2081632687 t = 0.2081632687 Simplifying t = 0.2081632687Subproblem 2
t + -0.2040816327 = -0.004081636 Simplifying t + -0.2040816327 = -0.004081636 Reorder the terms: -0.2040816327 + t = -0.004081636 Solving -0.2040816327 + t = -0.004081636 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 = -0.004081636 + 0.2040816327 Combine like terms: -0.2040816327 + 0.2040816327 = 0.0000000000 0.0000000000 + t = -0.004081636 + 0.2040816327 t = -0.004081636 + 0.2040816327 Combine like terms: -0.004081636 + 0.2040816327 = 0.1999999967 t = 0.1999999967 Simplifying t = 0.1999999967Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.2081632687, 0.1999999967}
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