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Simplifying 0 = -16t2 + 12t + -2.2 Reorder the terms: 0 = -2.2 + 12t + -16t2 Solving 0 = -2.2 + 12t + -16t2 Solving for variable 't'. Combine like terms: 0 + 2.2 = 2.2 2.2 + -12t + 16t2 = -2.2 + 12t + -16t2 + 2.2 + -12t + 16t2 Reorder the terms: 2.2 + -12t + 16t2 = -2.2 + 2.2 + 12t + -12t + -16t2 + 16t2 Combine like terms: -2.2 + 2.2 = 0.0 2.2 + -12t + 16t2 = 0.0 + 12t + -12t + -16t2 + 16t2 2.2 + -12t + 16t2 = 12t + -12t + -16t2 + 16t2 Combine like terms: 12t + -12t = 0 2.2 + -12t + 16t2 = 0 + -16t2 + 16t2 2.2 + -12t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 2.2 + -12t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.1375 + -0.75t + t2 = 0 Move the constant term to the right: Add '-0.1375' to each side of the equation. 0.1375 + -0.75t + -0.1375 + t2 = 0 + -0.1375 Reorder the terms: 0.1375 + -0.1375 + -0.75t + t2 = 0 + -0.1375 Combine like terms: 0.1375 + -0.1375 = 0.0000 0.0000 + -0.75t + t2 = 0 + -0.1375 -0.75t + t2 = 0 + -0.1375 Combine like terms: 0 + -0.1375 = -0.1375 -0.75t + t2 = -0.1375 The t term is -0.75t. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75t + 0.140625 + t2 = -0.1375 + 0.140625 Reorder the terms: 0.140625 + -0.75t + t2 = -0.1375 + 0.140625 Combine like terms: -0.1375 + 0.140625 = 0.003125 0.140625 + -0.75t + t2 = 0.003125 Factor a perfect square on the left side: (t + -0.375)(t + -0.375) = 0.003125 Calculate the square root of the right side: 0.055901699 Break this problem into two subproblems by setting (t + -0.375) equal to 0.055901699 and -0.055901699.Subproblem 1
t + -0.375 = 0.055901699 Simplifying t + -0.375 = 0.055901699 Reorder the terms: -0.375 + t = 0.055901699 Solving -0.375 + t = 0.055901699 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + t = 0.055901699 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + t = 0.055901699 + 0.375 t = 0.055901699 + 0.375 Combine like terms: 0.055901699 + 0.375 = 0.430901699 t = 0.430901699 Simplifying t = 0.430901699Subproblem 2
t + -0.375 = -0.055901699 Simplifying t + -0.375 = -0.055901699 Reorder the terms: -0.375 + t = -0.055901699 Solving -0.375 + t = -0.055901699 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + t = -0.055901699 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + t = -0.055901699 + 0.375 t = -0.055901699 + 0.375 Combine like terms: -0.055901699 + 0.375 = 0.319098301 t = 0.319098301 Simplifying t = 0.319098301Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.430901699, 0.319098301}
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