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Simplifying 60 = 3t2 + 36t Reorder the terms: 60 = 36t + 3t2 Solving 60 = 36t + 3t2 Solving for variable 't'. Reorder the terms: 60 + -36t + -3t2 = 36t + -36t + 3t2 + -3t2 Combine like terms: 36t + -36t = 0 60 + -36t + -3t2 = 0 + 3t2 + -3t2 60 + -36t + -3t2 = 3t2 + -3t2 Combine like terms: 3t2 + -3t2 = 0 60 + -36t + -3t2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(20 + -12t + -1t2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(20 + -12t + -1t2)' equal to zero and attempt to solve: Simplifying 20 + -12t + -1t2 = 0 Solving 20 + -12t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -20 + 12t + t2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + 12t + 20 + t2 = 0 + 20 Reorder the terms: -20 + 20 + 12t + t2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 12t + t2 = 0 + 20 12t + t2 = 0 + 20 Combine like terms: 0 + 20 = 20 12t + t2 = 20 The t term is 12t. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12t + 36 + t2 = 20 + 36 Reorder the terms: 36 + 12t + t2 = 20 + 36 Combine like terms: 20 + 36 = 56 36 + 12t + t2 = 56 Factor a perfect square on the left side: (t + 6)(t + 6) = 56 Calculate the square root of the right side: 7.483314774 Break this problem into two subproblems by setting (t + 6) equal to 7.483314774 and -7.483314774.Subproblem 1
t + 6 = 7.483314774 Simplifying t + 6 = 7.483314774 Reorder the terms: 6 + t = 7.483314774 Solving 6 + t = 7.483314774 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + t = 7.483314774 + -6 Combine like terms: 6 + -6 = 0 0 + t = 7.483314774 + -6 t = 7.483314774 + -6 Combine like terms: 7.483314774 + -6 = 1.483314774 t = 1.483314774 Simplifying t = 1.483314774Subproblem 2
t + 6 = -7.483314774 Simplifying t + 6 = -7.483314774 Reorder the terms: 6 + t = -7.483314774 Solving 6 + t = -7.483314774 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + t = -7.483314774 + -6 Combine like terms: 6 + -6 = 0 0 + t = -7.483314774 + -6 t = -7.483314774 + -6 Combine like terms: -7.483314774 + -6 = -13.483314774 t = -13.483314774 Simplifying t = -13.483314774Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.483314774, -13.483314774}Solution
t = {1.483314774, -13.483314774}
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