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Simplifying 0.00771t2 + 0.0004t + 0.0000028 = 1200 Reorder the terms: 0.0000028 + 0.0004t + 0.00771t2 = 1200 Solving 0.0000028 + 0.0004t + 0.00771t2 = 1200 Solving for variable 't'. Reorder the terms: 0.0000028 + -1200 + 0.0004t + 0.00771t2 = 1200 + -1200 Combine like terms: 0.0000028 + -1200 = -1199.9999972 -1199.9999972 + 0.0004t + 0.00771t2 = 1200 + -1200 Combine like terms: 1200 + -1200 = 0 -1199.9999972 + 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'. -155642.023 + 0.05188067445t + t2 = 0 Move the constant term to the right: Add '155642.023' to each side of the equation. -155642.023 + 0.05188067445t + 155642.023 + t2 = 0 + 155642.023 Reorder the terms: -155642.023 + 155642.023 + 0.05188067445t + t2 = 0 + 155642.023 Combine like terms: -155642.023 + 155642.023 = 0.000 0.000 + 0.05188067445t + t2 = 0 + 155642.023 0.05188067445t + t2 = 0 + 155642.023 Combine like terms: 0 + 155642.023 = 155642.023 0.05188067445t + t2 = 155642.023 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 = 155642.023 + 0.0006729010956 Reorder the terms: 0.0006729010956 + 0.05188067445t + t2 = 155642.023 + 0.0006729010956 Combine like terms: 155642.023 + 0.0006729010956 = 155642.0236729010956 0.0006729010956 + 0.05188067445t + t2 = 155642.0236729010956 Factor a perfect square on the left side: (t + 0.02594033723)(t + 0.02594033723) = 155642.0236729010956 Calculate the square root of the right side: 394.51492199 Break this problem into two subproblems by setting (t + 0.02594033723) equal to 394.51492199 and -394.51492199.Subproblem 1
t + 0.02594033723 = 394.51492199 Simplifying t + 0.02594033723 = 394.51492199 Reorder the terms: 0.02594033723 + t = 394.51492199 Solving 0.02594033723 + t = 394.51492199 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 = 394.51492199 + -0.02594033723 Combine like terms: 0.02594033723 + -0.02594033723 = 0.00000000000 0.00000000000 + t = 394.51492199 + -0.02594033723 t = 394.51492199 + -0.02594033723 Combine like terms: 394.51492199 + -0.02594033723 = 394.48898165277 t = 394.48898165277 Simplifying t = 394.48898165277Subproblem 2
t + 0.02594033723 = -394.51492199 Simplifying t + 0.02594033723 = -394.51492199 Reorder the terms: 0.02594033723 + t = -394.51492199 Solving 0.02594033723 + t = -394.51492199 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 = -394.51492199 + -0.02594033723 Combine like terms: 0.02594033723 + -0.02594033723 = 0.00000000000 0.00000000000 + t = -394.51492199 + -0.02594033723 t = -394.51492199 + -0.02594033723 Combine like terms: -394.51492199 + -0.02594033723 = -394.54086232723 t = -394.54086232723 Simplifying t = -394.54086232723Solution
The solution to the problem is based on the solutions from the subproblems. t = {394.48898165277, -394.54086232723}
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