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Simplifying 0 = -16t2 + -30t + 6 Reorder the terms: 0 = 6 + -30t + -16t2 Solving 0 = 6 + -30t + -16t2 Solving for variable 't'. Combine like terms: 0 + -6 = -6 -6 + 30t + 16t2 = 6 + -30t + -16t2 + -6 + 30t + 16t2 Reorder the terms: -6 + 30t + 16t2 = 6 + -6 + -30t + 30t + -16t2 + 16t2 Combine like terms: 6 + -6 = 0 -6 + 30t + 16t2 = 0 + -30t + 30t + -16t2 + 16t2 -6 + 30t + 16t2 = -30t + 30t + -16t2 + 16t2 Combine like terms: -30t + 30t = 0 -6 + 30t + 16t2 = 0 + -16t2 + 16t2 -6 + 30t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -6 + 30t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + 15t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + 15t + 8t2)' equal to zero and attempt to solve: Simplifying -3 + 15t + 8t2 = 0 Solving -3 + 15t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.375 + 1.875t + t2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + 1.875t + 0.375 + t2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + 1.875t + t2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + 1.875t + t2 = 0 + 0.375 1.875t + t2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 1.875t + t2 = 0.375 The t term is 1.875t. Take half its coefficient (0.9375). Square it (0.87890625) and add it to both sides. Add '0.87890625' to each side of the equation. 1.875t + 0.87890625 + t2 = 0.375 + 0.87890625 Reorder the terms: 0.87890625 + 1.875t + t2 = 0.375 + 0.87890625 Combine like terms: 0.375 + 0.87890625 = 1.25390625 0.87890625 + 1.875t + t2 = 1.25390625 Factor a perfect square on the left side: (t + 0.9375)(t + 0.9375) = 1.25390625 Calculate the square root of the right side: 1.119779554 Break this problem into two subproblems by setting (t + 0.9375) equal to 1.119779554 and -1.119779554.Subproblem 1
t + 0.9375 = 1.119779554 Simplifying t + 0.9375 = 1.119779554 Reorder the terms: 0.9375 + t = 1.119779554 Solving 0.9375 + t = 1.119779554 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.9375' to each side of the equation. 0.9375 + -0.9375 + t = 1.119779554 + -0.9375 Combine like terms: 0.9375 + -0.9375 = 0.0000 0.0000 + t = 1.119779554 + -0.9375 t = 1.119779554 + -0.9375 Combine like terms: 1.119779554 + -0.9375 = 0.182279554 t = 0.182279554 Simplifying t = 0.182279554Subproblem 2
t + 0.9375 = -1.119779554 Simplifying t + 0.9375 = -1.119779554 Reorder the terms: 0.9375 + t = -1.119779554 Solving 0.9375 + t = -1.119779554 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.9375' to each side of the equation. 0.9375 + -0.9375 + t = -1.119779554 + -0.9375 Combine like terms: 0.9375 + -0.9375 = 0.0000 0.0000 + t = -1.119779554 + -0.9375 t = -1.119779554 + -0.9375 Combine like terms: -1.119779554 + -0.9375 = -2.057279554 t = -2.057279554 Simplifying t = -2.057279554Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.182279554, -2.057279554}Solution
t = {0.182279554, -2.057279554}
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