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Simplifying 0.00771t2 + 0.0004t + 0.0000028 = 1050 Reorder the terms: 0.0000028 + 0.0004t + 0.00771t2 = 1050 Solving 0.0000028 + 0.0004t + 0.00771t2 = 1050 Solving for variable 't'. Reorder the terms: 0.0000028 + -1050 + 0.0004t + 0.00771t2 = 1050 + -1050 Combine like terms: 0.0000028 + -1050 = -1049.9999972 -1049.9999972 + 0.0004t + 0.00771t2 = 1050 + -1050 Combine like terms: 1050 + -1050 = 0 -1049.9999972 + 0.0004t + 0.00771t2 = 0 Begin completing the square. Divide all terms by 0.00771 the coefficient of the squared term: Divide each side by '0.00771'. -136186.7701 + 0.05188067445t + t2 = 0 Move the constant term to the right: Add '136186.7701' to each side of the equation. -136186.7701 + 0.05188067445t + 136186.7701 + t2 = 0 + 136186.7701 Reorder the terms: -136186.7701 + 136186.7701 + 0.05188067445t + t2 = 0 + 136186.7701 Combine like terms: -136186.7701 + 136186.7701 = 0.0000 0.0000 + 0.05188067445t + t2 = 0 + 136186.7701 0.05188067445t + t2 = 0 + 136186.7701 Combine like terms: 0 + 136186.7701 = 136186.7701 0.05188067445t + t2 = 136186.7701 The t term is 0.05188067445t. Take half its coefficient (0.02594033723). Square it (0.0006729010956) and add it to both sides. Add '0.0006729010956' to each side of the equation. 0.05188067445t + 0.0006729010956 + t2 = 136186.7701 + 0.0006729010956 Reorder the terms: 0.0006729010956 + 0.05188067445t + t2 = 136186.7701 + 0.0006729010956 Combine like terms: 136186.7701 + 0.0006729010956 = 136186.7707729010956 0.0006729010956 + 0.05188067445t + t2 = 136186.7707729010956 Factor a perfect square on the left side: (t + 0.02594033723)(t + 0.02594033723) = 136186.7707729010956 Calculate the square root of the right side: 369.034918094 Break this problem into two subproblems by setting (t + 0.02594033723) equal to 369.034918094 and -369.034918094.Subproblem 1
t + 0.02594033723 = 369.034918094 Simplifying t + 0.02594033723 = 369.034918094 Reorder the terms: 0.02594033723 + t = 369.034918094 Solving 0.02594033723 + t = 369.034918094 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.02594033723' to each side of the equation. 0.02594033723 + -0.02594033723 + t = 369.034918094 + -0.02594033723 Combine like terms: 0.02594033723 + -0.02594033723 = 0.00000000000 0.00000000000 + t = 369.034918094 + -0.02594033723 t = 369.034918094 + -0.02594033723 Combine like terms: 369.034918094 + -0.02594033723 = 369.00897775677 t = 369.00897775677 Simplifying t = 369.00897775677Subproblem 2
t + 0.02594033723 = -369.034918094 Simplifying t + 0.02594033723 = -369.034918094 Reorder the terms: 0.02594033723 + t = -369.034918094 Solving 0.02594033723 + t = -369.034918094 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.02594033723' to each side of the equation. 0.02594033723 + -0.02594033723 + t = -369.034918094 + -0.02594033723 Combine like terms: 0.02594033723 + -0.02594033723 = 0.00000000000 0.00000000000 + t = -369.034918094 + -0.02594033723 t = -369.034918094 + -0.02594033723 Combine like terms: -369.034918094 + -0.02594033723 = -369.06085843123 t = -369.06085843123 Simplifying t = -369.06085843123Solution
The solution to the problem is based on the solutions from the subproblems. t = {369.00897775677, -369.06085843123}
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