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Simplifying 6 = 12 + -5t + -4.9t2 Solving 6 = 12 + -5t + -4.9t2 Solving for variable 't'. Combine like terms: 6 + -12 = -6 -6 + 5t + 4.9t2 = 12 + -5t + -4.9t2 + -12 + 5t + 4.9t2 Reorder the terms: -6 + 5t + 4.9t2 = 12 + -12 + -5t + 5t + -4.9t2 + 4.9t2 Combine like terms: 12 + -12 = 0 -6 + 5t + 4.9t2 = 0 + -5t + 5t + -4.9t2 + 4.9t2 -6 + 5t + 4.9t2 = -5t + 5t + -4.9t2 + 4.9t2 Combine like terms: -5t + 5t = 0 -6 + 5t + 4.9t2 = 0 + -4.9t2 + 4.9t2 -6 + 5t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -6 + 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'. -1.224489796 + 1.020408163t + t2 = 0 Move the constant term to the right: Add '1.224489796' to each side of the equation. -1.224489796 + 1.020408163t + 1.224489796 + t2 = 0 + 1.224489796 Reorder the terms: -1.224489796 + 1.224489796 + 1.020408163t + t2 = 0 + 1.224489796 Combine like terms: -1.224489796 + 1.224489796 = 0.000000000 0.000000000 + 1.020408163t + t2 = 0 + 1.224489796 1.020408163t + t2 = 0 + 1.224489796 Combine like terms: 0 + 1.224489796 = 1.224489796 1.020408163t + t2 = 1.224489796 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 = 1.224489796 + 0.2603082048 Reorder the terms: 0.2603082048 + 1.020408163t + t2 = 1.224489796 + 0.2603082048 Combine like terms: 1.224489796 + 0.2603082048 = 1.4847980008 0.2603082048 + 1.020408163t + t2 = 1.4847980008 Factor a perfect square on the left side: (t + 0.5102040815)(t + 0.5102040815) = 1.4847980008 Calculate the square root of the right side: 1.218522877 Break this problem into two subproblems by setting (t + 0.5102040815) equal to 1.218522877 and -1.218522877.Subproblem 1
t + 0.5102040815 = 1.218522877 Simplifying t + 0.5102040815 = 1.218522877 Reorder the terms: 0.5102040815 + t = 1.218522877 Solving 0.5102040815 + t = 1.218522877 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 = 1.218522877 + -0.5102040815 Combine like terms: 0.5102040815 + -0.5102040815 = 0.0000000000 0.0000000000 + t = 1.218522877 + -0.5102040815 t = 1.218522877 + -0.5102040815 Combine like terms: 1.218522877 + -0.5102040815 = 0.7083187955 t = 0.7083187955 Simplifying t = 0.7083187955Subproblem 2
t + 0.5102040815 = -1.218522877 Simplifying t + 0.5102040815 = -1.218522877 Reorder the terms: 0.5102040815 + t = -1.218522877 Solving 0.5102040815 + t = -1.218522877 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 = -1.218522877 + -0.5102040815 Combine like terms: 0.5102040815 + -0.5102040815 = 0.0000000000 0.0000000000 + t = -1.218522877 + -0.5102040815 t = -1.218522877 + -0.5102040815 Combine like terms: -1.218522877 + -0.5102040815 = -1.7287269585 t = -1.7287269585 Simplifying t = -1.7287269585Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.7083187955, -1.7287269585}
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