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Simplifying 0 = -16t2 + 60t + 82 Reorder the terms: 0 = 82 + 60t + -16t2 Solving 0 = 82 + 60t + -16t2 Solving for variable 't'. Combine like terms: 0 + -82 = -82 -82 + -60t + 16t2 = 82 + 60t + -16t2 + -82 + -60t + 16t2 Reorder the terms: -82 + -60t + 16t2 = 82 + -82 + 60t + -60t + -16t2 + 16t2 Combine like terms: 82 + -82 = 0 -82 + -60t + 16t2 = 0 + 60t + -60t + -16t2 + 16t2 -82 + -60t + 16t2 = 60t + -60t + -16t2 + 16t2 Combine like terms: 60t + -60t = 0 -82 + -60t + 16t2 = 0 + -16t2 + 16t2 -82 + -60t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -82 + -60t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-41 + -30t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-41 + -30t + 8t2)' equal to zero and attempt to solve: Simplifying -41 + -30t + 8t2 = 0 Solving -41 + -30t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -5.125 + -3.75t + t2 = 0 Move the constant term to the right: Add '5.125' to each side of the equation. -5.125 + -3.75t + 5.125 + t2 = 0 + 5.125 Reorder the terms: -5.125 + 5.125 + -3.75t + t2 = 0 + 5.125 Combine like terms: -5.125 + 5.125 = 0.000 0.000 + -3.75t + t2 = 0 + 5.125 -3.75t + t2 = 0 + 5.125 Combine like terms: 0 + 5.125 = 5.125 -3.75t + t2 = 5.125 The t term is -3.75t. Take half its coefficient (-1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. -3.75t + 3.515625 + t2 = 5.125 + 3.515625 Reorder the terms: 3.515625 + -3.75t + t2 = 5.125 + 3.515625 Combine like terms: 5.125 + 3.515625 = 8.640625 3.515625 + -3.75t + t2 = 8.640625 Factor a perfect square on the left side: (t + -1.875)(t + -1.875) = 8.640625 Calculate the square root of the right side: 2.939494004 Break this problem into two subproblems by setting (t + -1.875) equal to 2.939494004 and -2.939494004.Subproblem 1
t + -1.875 = 2.939494004 Simplifying t + -1.875 = 2.939494004 Reorder the terms: -1.875 + t = 2.939494004 Solving -1.875 + t = 2.939494004 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + t = 2.939494004 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + t = 2.939494004 + 1.875 t = 2.939494004 + 1.875 Combine like terms: 2.939494004 + 1.875 = 4.814494004 t = 4.814494004 Simplifying t = 4.814494004Subproblem 2
t + -1.875 = -2.939494004 Simplifying t + -1.875 = -2.939494004 Reorder the terms: -1.875 + t = -2.939494004 Solving -1.875 + t = -2.939494004 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + t = -2.939494004 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + t = -2.939494004 + 1.875 t = -2.939494004 + 1.875 Combine like terms: -2.939494004 + 1.875 = -1.064494004 t = -1.064494004 Simplifying t = -1.064494004Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.814494004, -1.064494004}Solution
t = {4.814494004, -1.064494004}
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