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Simplifying 0 = 130 + -6t + -16t2 Solving 0 = 130 + -6t + -16t2 Solving for variable 't'. Combine like terms: 0 + -130 = -130 -130 + 6t + 16t2 = 130 + -6t + -16t2 + -130 + 6t + 16t2 Reorder the terms: -130 + 6t + 16t2 = 130 + -130 + -6t + 6t + -16t2 + 16t2 Combine like terms: 130 + -130 = 0 -130 + 6t + 16t2 = 0 + -6t + 6t + -16t2 + 16t2 -130 + 6t + 16t2 = -6t + 6t + -16t2 + 16t2 Combine like terms: -6t + 6t = 0 -130 + 6t + 16t2 = 0 + -16t2 + 16t2 -130 + 6t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -130 + 6t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-65 + 3t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-65 + 3t + 8t2)' equal to zero and attempt to solve: Simplifying -65 + 3t + 8t2 = 0 Solving -65 + 3t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -8.125 + 0.375t + t2 = 0 Move the constant term to the right: Add '8.125' to each side of the equation. -8.125 + 0.375t + 8.125 + t2 = 0 + 8.125 Reorder the terms: -8.125 + 8.125 + 0.375t + t2 = 0 + 8.125 Combine like terms: -8.125 + 8.125 = 0.000 0.000 + 0.375t + t2 = 0 + 8.125 0.375t + t2 = 0 + 8.125 Combine like terms: 0 + 8.125 = 8.125 0.375t + t2 = 8.125 The t term is 0.375t. Take half its coefficient (0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. 0.375t + 0.03515625 + t2 = 8.125 + 0.03515625 Reorder the terms: 0.03515625 + 0.375t + t2 = 8.125 + 0.03515625 Combine like terms: 8.125 + 0.03515625 = 8.16015625 0.03515625 + 0.375t + t2 = 8.16015625 Factor a perfect square on the left side: (t + 0.1875)(t + 0.1875) = 8.16015625 Calculate the square root of the right side: 2.856598721 Break this problem into two subproblems by setting (t + 0.1875) equal to 2.856598721 and -2.856598721.Subproblem 1
t + 0.1875 = 2.856598721 Simplifying t + 0.1875 = 2.856598721 Reorder the terms: 0.1875 + t = 2.856598721 Solving 0.1875 + t = 2.856598721 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + t = 2.856598721 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + t = 2.856598721 + -0.1875 t = 2.856598721 + -0.1875 Combine like terms: 2.856598721 + -0.1875 = 2.669098721 t = 2.669098721 Simplifying t = 2.669098721Subproblem 2
t + 0.1875 = -2.856598721 Simplifying t + 0.1875 = -2.856598721 Reorder the terms: 0.1875 + t = -2.856598721 Solving 0.1875 + t = -2.856598721 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + t = -2.856598721 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + t = -2.856598721 + -0.1875 t = -2.856598721 + -0.1875 Combine like terms: -2.856598721 + -0.1875 = -3.044098721 t = -3.044098721 Simplifying t = -3.044098721Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.669098721, -3.044098721}Solution
t = {2.669098721, -3.044098721}
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