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Simplifying 10 = 6.6 + 46t + -16t2 Solving 10 = 6.6 + 46t + -16t2 Solving for variable 't'. Combine like terms: 10 + -6.6 = 3.4 3.4 + -46t + 16t2 = 6.6 + 46t + -16t2 + -6.6 + -46t + 16t2 Reorder the terms: 3.4 + -46t + 16t2 = 6.6 + -6.6 + 46t + -46t + -16t2 + 16t2 Combine like terms: 6.6 + -6.6 = 0.0 3.4 + -46t + 16t2 = 0.0 + 46t + -46t + -16t2 + 16t2 3.4 + -46t + 16t2 = 46t + -46t + -16t2 + 16t2 Combine like terms: 46t + -46t = 0 3.4 + -46t + 16t2 = 0 + -16t2 + 16t2 3.4 + -46t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 3.4 + -46t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.2125 + -2.875t + t2 = 0 Move the constant term to the right: Add '-0.2125' to each side of the equation. 0.2125 + -2.875t + -0.2125 + t2 = 0 + -0.2125 Reorder the terms: 0.2125 + -0.2125 + -2.875t + t2 = 0 + -0.2125 Combine like terms: 0.2125 + -0.2125 = 0.0000 0.0000 + -2.875t + t2 = 0 + -0.2125 -2.875t + t2 = 0 + -0.2125 Combine like terms: 0 + -0.2125 = -0.2125 -2.875t + t2 = -0.2125 The t term is -2.875t. Take half its coefficient (-1.4375). Square it (2.06640625) and add it to both sides. Add '2.06640625' to each side of the equation. -2.875t + 2.06640625 + t2 = -0.2125 + 2.06640625 Reorder the terms: 2.06640625 + -2.875t + t2 = -0.2125 + 2.06640625 Combine like terms: -0.2125 + 2.06640625 = 1.85390625 2.06640625 + -2.875t + t2 = 1.85390625 Factor a perfect square on the left side: (t + -1.4375)(t + -1.4375) = 1.85390625 Calculate the square root of the right side: 1.36158226 Break this problem into two subproblems by setting (t + -1.4375) equal to 1.36158226 and -1.36158226.Subproblem 1
t + -1.4375 = 1.36158226 Simplifying t + -1.4375 = 1.36158226 Reorder the terms: -1.4375 + t = 1.36158226 Solving -1.4375 + t = 1.36158226 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.4375' to each side of the equation. -1.4375 + 1.4375 + t = 1.36158226 + 1.4375 Combine like terms: -1.4375 + 1.4375 = 0.0000 0.0000 + t = 1.36158226 + 1.4375 t = 1.36158226 + 1.4375 Combine like terms: 1.36158226 + 1.4375 = 2.79908226 t = 2.79908226 Simplifying t = 2.79908226Subproblem 2
t + -1.4375 = -1.36158226 Simplifying t + -1.4375 = -1.36158226 Reorder the terms: -1.4375 + t = -1.36158226 Solving -1.4375 + t = -1.36158226 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.4375' to each side of the equation. -1.4375 + 1.4375 + t = -1.36158226 + 1.4375 Combine like terms: -1.4375 + 1.4375 = 0.0000 0.0000 + t = -1.36158226 + 1.4375 t = -1.36158226 + 1.4375 Combine like terms: -1.36158226 + 1.4375 = 0.07591774 t = 0.07591774 Simplifying t = 0.07591774Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.79908226, 0.07591774}
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