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Simplifying 0 = 2 + 5t + -4.9t2 Solving 0 = 2 + 5t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -2 = -2 -2 + -5t + 4.9t2 = 2 + 5t + -4.9t2 + -2 + -5t + 4.9t2 Reorder the terms: -2 + -5t + 4.9t2 = 2 + -2 + 5t + -5t + -4.9t2 + 4.9t2 Combine like terms: 2 + -2 = 0 -2 + -5t + 4.9t2 = 0 + 5t + -5t + -4.9t2 + 4.9t2 -2 + -5t + 4.9t2 = 5t + -5t + -4.9t2 + 4.9t2 Combine like terms: 5t + -5t = 0 -2 + -5t + 4.9t2 = 0 + -4.9t2 + 4.9t2 -2 + -5t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -2 + -5t + 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 + -1.020408163t + t2 = 0 Move the constant term to the right: Add '0.4081632653' to each side of the equation. -0.4081632653 + -1.020408163t + 0.4081632653 + t2 = 0 + 0.4081632653 Reorder the terms: -0.4081632653 + 0.4081632653 + -1.020408163t + t2 = 0 + 0.4081632653 Combine like terms: -0.4081632653 + 0.4081632653 = 0.0000000000 0.0000000000 + -1.020408163t + t2 = 0 + 0.4081632653 -1.020408163t + t2 = 0 + 0.4081632653 Combine like terms: 0 + 0.4081632653 = 0.4081632653 -1.020408163t + t2 = 0.4081632653 The t term is -1.020408163t. Take half its coefficient (-0.5102040815). Square it (0.2603082048) and add it to both sides. Add '0.2603082048' to each side of the equation. -1.020408163t + 0.2603082048 + t2 = 0.4081632653 + 0.2603082048 Reorder the terms: 0.2603082048 + -1.020408163t + t2 = 0.4081632653 + 0.2603082048 Combine like terms: 0.4081632653 + 0.2603082048 = 0.6684714701 0.2603082048 + -1.020408163t + t2 = 0.6684714701 Factor a perfect square on the left side: (t + -0.5102040815)(t + -0.5102040815) = 0.6684714701 Calculate the square root of the right side: 0.817601046 Break this problem into two subproblems by setting (t + -0.5102040815) equal to 0.817601046 and -0.817601046.Subproblem 1
t + -0.5102040815 = 0.817601046 Simplifying t + -0.5102040815 = 0.817601046 Reorder the terms: -0.5102040815 + t = 0.817601046 Solving -0.5102040815 + t = 0.817601046 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5102040815' to each side of the equation. -0.5102040815 + 0.5102040815 + t = 0.817601046 + 0.5102040815 Combine like terms: -0.5102040815 + 0.5102040815 = 0.0000000000 0.0000000000 + t = 0.817601046 + 0.5102040815 t = 0.817601046 + 0.5102040815 Combine like terms: 0.817601046 + 0.5102040815 = 1.3278051275 t = 1.3278051275 Simplifying t = 1.3278051275Subproblem 2
t + -0.5102040815 = -0.817601046 Simplifying t + -0.5102040815 = -0.817601046 Reorder the terms: -0.5102040815 + t = -0.817601046 Solving -0.5102040815 + t = -0.817601046 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5102040815' to each side of the equation. -0.5102040815 + 0.5102040815 + t = -0.817601046 + 0.5102040815 Combine like terms: -0.5102040815 + 0.5102040815 = 0.0000000000 0.0000000000 + t = -0.817601046 + 0.5102040815 t = -0.817601046 + 0.5102040815 Combine like terms: -0.817601046 + 0.5102040815 = -0.3073969645 t = -0.3073969645 Simplifying t = -0.3073969645Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.3278051275, -0.3073969645}
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