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Simplifying 0 = -7t2 + -76t + -11 Reorder the terms: 0 = -11 + -76t + -7t2 Solving 0 = -11 + -76t + -7t2 Solving for variable 't'. Combine like terms: 0 + 11 = 11 11 + 76t + 7t2 = -11 + -76t + -7t2 + 11 + 76t + 7t2 Reorder the terms: 11 + 76t + 7t2 = -11 + 11 + -76t + 76t + -7t2 + 7t2 Combine like terms: -11 + 11 = 0 11 + 76t + 7t2 = 0 + -76t + 76t + -7t2 + 7t2 11 + 76t + 7t2 = -76t + 76t + -7t2 + 7t2 Combine like terms: -76t + 76t = 0 11 + 76t + 7t2 = 0 + -7t2 + 7t2 11 + 76t + 7t2 = -7t2 + 7t2 Combine like terms: -7t2 + 7t2 = 0 11 + 76t + 7t2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 1.571428571 + 10.85714286t + t2 = 0 Move the constant term to the right: Add '-1.571428571' to each side of the equation. 1.571428571 + 10.85714286t + -1.571428571 + t2 = 0 + -1.571428571 Reorder the terms: 1.571428571 + -1.571428571 + 10.85714286t + t2 = 0 + -1.571428571 Combine like terms: 1.571428571 + -1.571428571 = 0.000000000 0.000000000 + 10.85714286t + t2 = 0 + -1.571428571 10.85714286t + t2 = 0 + -1.571428571 Combine like terms: 0 + -1.571428571 = -1.571428571 10.85714286t + t2 = -1.571428571 The t term is 10.85714286t. Take half its coefficient (5.42857143). Square it (29.46938777) and add it to both sides. Add '29.46938777' to each side of the equation. 10.85714286t + 29.46938777 + t2 = -1.571428571 + 29.46938777 Reorder the terms: 29.46938777 + 10.85714286t + t2 = -1.571428571 + 29.46938777 Combine like terms: -1.571428571 + 29.46938777 = 27.897959199 29.46938777 + 10.85714286t + t2 = 27.897959199 Factor a perfect square on the left side: (t + 5.42857143)(t + 5.42857143) = 27.897959199 Calculate the square root of the right side: 5.281851872 Break this problem into two subproblems by setting (t + 5.42857143) equal to 5.281851872 and -5.281851872.Subproblem 1
t + 5.42857143 = 5.281851872 Simplifying t + 5.42857143 = 5.281851872 Reorder the terms: 5.42857143 + t = 5.281851872 Solving 5.42857143 + t = 5.281851872 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-5.42857143' to each side of the equation. 5.42857143 + -5.42857143 + t = 5.281851872 + -5.42857143 Combine like terms: 5.42857143 + -5.42857143 = 0.00000000 0.00000000 + t = 5.281851872 + -5.42857143 t = 5.281851872 + -5.42857143 Combine like terms: 5.281851872 + -5.42857143 = -0.146719558 t = -0.146719558 Simplifying t = -0.146719558Subproblem 2
t + 5.42857143 = -5.281851872 Simplifying t + 5.42857143 = -5.281851872 Reorder the terms: 5.42857143 + t = -5.281851872 Solving 5.42857143 + t = -5.281851872 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-5.42857143' to each side of the equation. 5.42857143 + -5.42857143 + t = -5.281851872 + -5.42857143 Combine like terms: 5.42857143 + -5.42857143 = 0.00000000 0.00000000 + t = -5.281851872 + -5.42857143 t = -5.281851872 + -5.42857143 Combine like terms: -5.281851872 + -5.42857143 = -10.710423302 t = -10.710423302 Simplifying t = -10.710423302Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.146719558, -10.710423302}
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