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Simplifying 2.7t2 + -13t + 5 = 3 Reorder the terms: 5 + -13t + 2.7t2 = 3 Solving 5 + -13t + 2.7t2 = 3 Solving for variable 't'. Reorder the terms: 5 + -3 + -13t + 2.7t2 = 3 + -3 Combine like terms: 5 + -3 = 2 2 + -13t + 2.7t2 = 3 + -3 Combine like terms: 3 + -3 = 0 2 + -13t + 2.7t2 = 0 Begin completing the square. Divide all terms by 2.7 the coefficient of the squared term: Divide each side by '2.7'. 0.7407407407 + -4.814814815t + t2 = 0 Move the constant term to the right: Add '-0.7407407407' to each side of the equation. 0.7407407407 + -4.814814815t + -0.7407407407 + t2 = 0 + -0.7407407407 Reorder the terms: 0.7407407407 + -0.7407407407 + -4.814814815t + t2 = 0 + -0.7407407407 Combine like terms: 0.7407407407 + -0.7407407407 = 0.0000000000 0.0000000000 + -4.814814815t + t2 = 0 + -0.7407407407 -4.814814815t + t2 = 0 + -0.7407407407 Combine like terms: 0 + -0.7407407407 = -0.7407407407 -4.814814815t + t2 = -0.7407407407 The t term is -4.814814815t. Take half its coefficient (-2.407407408). Square it (5.795610428) and add it to both sides. Add '5.795610428' to each side of the equation. -4.814814815t + 5.795610428 + t2 = -0.7407407407 + 5.795610428 Reorder the terms: 5.795610428 + -4.814814815t + t2 = -0.7407407407 + 5.795610428 Combine like terms: -0.7407407407 + 5.795610428 = 5.0548696873 5.795610428 + -4.814814815t + t2 = 5.0548696873 Factor a perfect square on the left side: (t + -2.407407408)(t + -2.407407408) = 5.0548696873 Calculate the square root of the right side: 2.248303736 Break this problem into two subproblems by setting (t + -2.407407408) equal to 2.248303736 and -2.248303736.Subproblem 1
t + -2.407407408 = 2.248303736 Simplifying t + -2.407407408 = 2.248303736 Reorder the terms: -2.407407408 + t = 2.248303736 Solving -2.407407408 + t = 2.248303736 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.407407408' to each side of the equation. -2.407407408 + 2.407407408 + t = 2.248303736 + 2.407407408 Combine like terms: -2.407407408 + 2.407407408 = 0.000000000 0.000000000 + t = 2.248303736 + 2.407407408 t = 2.248303736 + 2.407407408 Combine like terms: 2.248303736 + 2.407407408 = 4.655711144 t = 4.655711144 Simplifying t = 4.655711144Subproblem 2
t + -2.407407408 = -2.248303736 Simplifying t + -2.407407408 = -2.248303736 Reorder the terms: -2.407407408 + t = -2.248303736 Solving -2.407407408 + t = -2.248303736 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.407407408' to each side of the equation. -2.407407408 + 2.407407408 + t = -2.248303736 + 2.407407408 Combine like terms: -2.407407408 + 2.407407408 = 0.000000000 0.000000000 + t = -2.248303736 + 2.407407408 t = -2.248303736 + 2.407407408 Combine like terms: -2.248303736 + 2.407407408 = 0.159103672 t = 0.159103672 Simplifying t = 0.159103672Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.655711144, 0.159103672}
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