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Simplifying 2.6 = -2.7t + 9.8t2 Solving 2.6 = -2.7t + 9.8t2 Solving for variable 't'. Reorder the terms: 2.6 + 2.7t + -9.8t2 = -2.7t + 2.7t + 9.8t2 + -9.8t2 Combine like terms: -2.7t + 2.7t = 0.0 2.6 + 2.7t + -9.8t2 = 0.0 + 9.8t2 + -9.8t2 2.6 + 2.7t + -9.8t2 = 9.8t2 + -9.8t2 Combine like terms: 9.8t2 + -9.8t2 = 0.0 2.6 + 2.7t + -9.8t2 = 0.0 Begin completing the square. Divide all terms by -9.8 the coefficient of the squared term: Divide each side by '-9.8'. -0.2653061224 + -0.2755102041t + t2 = 0 Move the constant term to the right: Add '0.2653061224' to each side of the equation. -0.2653061224 + -0.2755102041t + 0.2653061224 + t2 = 0 + 0.2653061224 Reorder the terms: -0.2653061224 + 0.2653061224 + -0.2755102041t + t2 = 0 + 0.2653061224 Combine like terms: -0.2653061224 + 0.2653061224 = 0.0000000000 0.0000000000 + -0.2755102041t + t2 = 0 + 0.2653061224 -0.2755102041t + t2 = 0 + 0.2653061224 Combine like terms: 0 + 0.2653061224 = 0.2653061224 -0.2755102041t + t2 = 0.2653061224 The t term is -0.2755102041t. Take half its coefficient (-0.1377551021). Square it (0.01897646815) and add it to both sides. Add '0.01897646815' to each side of the equation. -0.2755102041t + 0.01897646815 + t2 = 0.2653061224 + 0.01897646815 Reorder the terms: 0.01897646815 + -0.2755102041t + t2 = 0.2653061224 + 0.01897646815 Combine like terms: 0.2653061224 + 0.01897646815 = 0.28428259055 0.01897646815 + -0.2755102041t + t2 = 0.28428259055 Factor a perfect square on the left side: (t + -0.1377551021)(t + -0.1377551021) = 0.28428259055 Calculate the square root of the right side: 0.533181574 Break this problem into two subproblems by setting (t + -0.1377551021) equal to 0.533181574 and -0.533181574.Subproblem 1
t + -0.1377551021 = 0.533181574 Simplifying t + -0.1377551021 = 0.533181574 Reorder the terms: -0.1377551021 + t = 0.533181574 Solving -0.1377551021 + t = 0.533181574 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.1377551021' to each side of the equation. -0.1377551021 + 0.1377551021 + t = 0.533181574 + 0.1377551021 Combine like terms: -0.1377551021 + 0.1377551021 = 0.0000000000 0.0000000000 + t = 0.533181574 + 0.1377551021 t = 0.533181574 + 0.1377551021 Combine like terms: 0.533181574 + 0.1377551021 = 0.6709366761 t = 0.6709366761 Simplifying t = 0.6709366761Subproblem 2
t + -0.1377551021 = -0.533181574 Simplifying t + -0.1377551021 = -0.533181574 Reorder the terms: -0.1377551021 + t = -0.533181574 Solving -0.1377551021 + t = -0.533181574 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.1377551021' to each side of the equation. -0.1377551021 + 0.1377551021 + t = -0.533181574 + 0.1377551021 Combine like terms: -0.1377551021 + 0.1377551021 = 0.0000000000 0.0000000000 + t = -0.533181574 + 0.1377551021 t = -0.533181574 + 0.1377551021 Combine like terms: -0.533181574 + 0.1377551021 = -0.3954264719 t = -0.3954264719 Simplifying t = -0.3954264719Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.6709366761, -0.3954264719}
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