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Simplifying 0 = 2 + 6t + -4.9t2 Solving 0 = 2 + 6t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -2 = -2 -2 + -6t + 4.9t2 = 2 + 6t + -4.9t2 + -2 + -6t + 4.9t2 Reorder the terms: -2 + -6t + 4.9t2 = 2 + -2 + 6t + -6t + -4.9t2 + 4.9t2 Combine like terms: 2 + -2 = 0 -2 + -6t + 4.9t2 = 0 + 6t + -6t + -4.9t2 + 4.9t2 -2 + -6t + 4.9t2 = 6t + -6t + -4.9t2 + 4.9t2 Combine like terms: 6t + -6t = 0 -2 + -6t + 4.9t2 = 0 + -4.9t2 + 4.9t2 -2 + -6t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -2 + -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'. -0.4081632653 + -1.224489796t + t2 = 0 Move the constant term to the right: Add '0.4081632653' to each side of the equation. -0.4081632653 + -1.224489796t + 0.4081632653 + t2 = 0 + 0.4081632653 Reorder the terms: -0.4081632653 + 0.4081632653 + -1.224489796t + t2 = 0 + 0.4081632653 Combine like terms: -0.4081632653 + 0.4081632653 = 0.0000000000 0.0000000000 + -1.224489796t + t2 = 0 + 0.4081632653 -1.224489796t + t2 = 0 + 0.4081632653 Combine like terms: 0 + 0.4081632653 = 0.4081632653 -1.224489796t + t2 = 0.4081632653 The t term is -1.224489796t. Take half its coefficient (-0.612244898). Square it (0.3748438151) and add it to both sides. Add '0.3748438151' to each side of the equation. -1.224489796t + 0.3748438151 + t2 = 0.4081632653 + 0.3748438151 Reorder the terms: 0.3748438151 + -1.224489796t + t2 = 0.4081632653 + 0.3748438151 Combine like terms: 0.4081632653 + 0.3748438151 = 0.7830070804 0.3748438151 + -1.224489796t + t2 = 0.7830070804 Factor a perfect square on the left side: (t + -0.612244898)(t + -0.612244898) = 0.7830070804 Calculate the square root of the right side: 0.884876873 Break this problem into two subproblems by setting (t + -0.612244898) equal to 0.884876873 and -0.884876873.Subproblem 1
t + -0.612244898 = 0.884876873 Simplifying t + -0.612244898 = 0.884876873 Reorder the terms: -0.612244898 + t = 0.884876873 Solving -0.612244898 + t = 0.884876873 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.612244898' to each side of the equation. -0.612244898 + 0.612244898 + t = 0.884876873 + 0.612244898 Combine like terms: -0.612244898 + 0.612244898 = 0.000000000 0.000000000 + t = 0.884876873 + 0.612244898 t = 0.884876873 + 0.612244898 Combine like terms: 0.884876873 + 0.612244898 = 1.497121771 t = 1.497121771 Simplifying t = 1.497121771Subproblem 2
t + -0.612244898 = -0.884876873 Simplifying t + -0.612244898 = -0.884876873 Reorder the terms: -0.612244898 + t = -0.884876873 Solving -0.612244898 + t = -0.884876873 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.612244898' to each side of the equation. -0.612244898 + 0.612244898 + t = -0.884876873 + 0.612244898 Combine like terms: -0.612244898 + 0.612244898 = 0.000000000 0.000000000 + t = -0.884876873 + 0.612244898 t = -0.884876873 + 0.612244898 Combine like terms: -0.884876873 + 0.612244898 = -0.272631975 t = -0.272631975 Simplifying t = -0.272631975Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.497121771, -0.272631975}
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