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Simplifying 130 = 96t + -16t2 Solving 130 = 96t + -16t2 Solving for variable 't'. Reorder the terms: 130 + -96t + 16t2 = 96t + -96t + -16t2 + 16t2 Combine like terms: 96t + -96t = 0 130 + -96t + 16t2 = 0 + -16t2 + 16t2 130 + -96t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 130 + -96t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(65 + -48t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(65 + -48t + 8t2)' equal to zero and attempt to solve: Simplifying 65 + -48t + 8t2 = 0 Solving 65 + -48t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 8.125 + -6t + t2 = 0 Move the constant term to the right: Add '-8.125' to each side of the equation. 8.125 + -6t + -8.125 + t2 = 0 + -8.125 Reorder the terms: 8.125 + -8.125 + -6t + t2 = 0 + -8.125 Combine like terms: 8.125 + -8.125 = 0.000 0.000 + -6t + t2 = 0 + -8.125 -6t + t2 = 0 + -8.125 Combine like terms: 0 + -8.125 = -8.125 -6t + t2 = -8.125 The t term is -6t. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6t + 9 + t2 = -8.125 + 9 Reorder the terms: 9 + -6t + t2 = -8.125 + 9 Combine like terms: -8.125 + 9 = 0.875 9 + -6t + t2 = 0.875 Factor a perfect square on the left side: (t + -3)(t + -3) = 0.875 Calculate the square root of the right side: 0.935414347 Break this problem into two subproblems by setting (t + -3) equal to 0.935414347 and -0.935414347.Subproblem 1
t + -3 = 0.935414347 Simplifying t + -3 = 0.935414347 Reorder the terms: -3 + t = 0.935414347 Solving -3 + t = 0.935414347 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = 0.935414347 + 3 Combine like terms: -3 + 3 = 0 0 + t = 0.935414347 + 3 t = 0.935414347 + 3 Combine like terms: 0.935414347 + 3 = 3.935414347 t = 3.935414347 Simplifying t = 3.935414347Subproblem 2
t + -3 = -0.935414347 Simplifying t + -3 = -0.935414347 Reorder the terms: -3 + t = -0.935414347 Solving -3 + t = -0.935414347 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = -0.935414347 + 3 Combine like terms: -3 + 3 = 0 0 + t = -0.935414347 + 3 t = -0.935414347 + 3 Combine like terms: -0.935414347 + 3 = 2.064585653 t = 2.064585653 Simplifying t = 2.064585653Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.935414347, 2.064585653}Solution
t = {3.935414347, 2.064585653}
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