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Simplifying 0.00771t2 + 0.0004t + 0.0000028 = 960 Reorder the terms: 0.0000028 + 0.0004t + 0.00771t2 = 960 Solving 0.0000028 + 0.0004t + 0.00771t2 = 960 Solving for variable 't'. Reorder the terms: 0.0000028 + -960 + 0.0004t + 0.00771t2 = 960 + -960 Combine like terms: 0.0000028 + -960 = -959.9999972 -959.9999972 + 0.0004t + 0.00771t2 = 960 + -960 Combine like terms: 960 + -960 = 0 -959.9999972 + 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'. -124513.6183 + 0.05188067445t + t2 = 0 Move the constant term to the right: Add '124513.6183' to each side of the equation. -124513.6183 + 0.05188067445t + 124513.6183 + t2 = 0 + 124513.6183 Reorder the terms: -124513.6183 + 124513.6183 + 0.05188067445t + t2 = 0 + 124513.6183 Combine like terms: -124513.6183 + 124513.6183 = 0.0000 0.0000 + 0.05188067445t + t2 = 0 + 124513.6183 0.05188067445t + t2 = 0 + 124513.6183 Combine like terms: 0 + 124513.6183 = 124513.6183 0.05188067445t + t2 = 124513.6183 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 = 124513.6183 + 0.0006729010956 Reorder the terms: 0.0006729010956 + 0.05188067445t + t2 = 124513.6183 + 0.0006729010956 Combine like terms: 124513.6183 + 0.0006729010956 = 124513.6189729010956 0.0006729010956 + 0.05188067445t + t2 = 124513.6189729010956 Factor a perfect square on the left side: (t + 0.02594033723)(t + 0.02594033723) = 124513.6189729010956 Calculate the square root of the right side: 352.864873532 Break this problem into two subproblems by setting (t + 0.02594033723) equal to 352.864873532 and -352.864873532.Subproblem 1
t + 0.02594033723 = 352.864873532 Simplifying t + 0.02594033723 = 352.864873532 Reorder the terms: 0.02594033723 + t = 352.864873532 Solving 0.02594033723 + t = 352.864873532 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 = 352.864873532 + -0.02594033723 Combine like terms: 0.02594033723 + -0.02594033723 = 0.00000000000 0.00000000000 + t = 352.864873532 + -0.02594033723 t = 352.864873532 + -0.02594033723 Combine like terms: 352.864873532 + -0.02594033723 = 352.83893319477 t = 352.83893319477 Simplifying t = 352.83893319477Subproblem 2
t + 0.02594033723 = -352.864873532 Simplifying t + 0.02594033723 = -352.864873532 Reorder the terms: 0.02594033723 + t = -352.864873532 Solving 0.02594033723 + t = -352.864873532 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 = -352.864873532 + -0.02594033723 Combine like terms: 0.02594033723 + -0.02594033723 = 0.00000000000 0.00000000000 + t = -352.864873532 + -0.02594033723 t = -352.864873532 + -0.02594033723 Combine like terms: -352.864873532 + -0.02594033723 = -352.89081386923 t = -352.89081386923 Simplifying t = -352.89081386923Solution
The solution to the problem is based on the solutions from the subproblems. t = {352.83893319477, -352.89081386923}
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