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Simplifying 2t2 + -12t + -60 = 0 Reorder the terms: -60 + -12t + 2t2 = 0 Solving -60 + -12t + 2t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(-30 + -6t + t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-30 + -6t + t2)' equal to zero and attempt to solve: Simplifying -30 + -6t + t2 = 0 Solving -30 + -6t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '30' to each side of the equation. -30 + -6t + 30 + t2 = 0 + 30 Reorder the terms: -30 + 30 + -6t + t2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + -6t + t2 = 0 + 30 -6t + t2 = 0 + 30 Combine like terms: 0 + 30 = 30 -6t + t2 = 30 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 = 30 + 9 Reorder the terms: 9 + -6t + t2 = 30 + 9 Combine like terms: 30 + 9 = 39 9 + -6t + t2 = 39 Factor a perfect square on the left side: (t + -3)(t + -3) = 39 Calculate the square root of the right side: 6.244997998 Break this problem into two subproblems by setting (t + -3) equal to 6.244997998 and -6.244997998.Subproblem 1
t + -3 = 6.244997998 Simplifying t + -3 = 6.244997998 Reorder the terms: -3 + t = 6.244997998 Solving -3 + t = 6.244997998 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 = 6.244997998 + 3 Combine like terms: -3 + 3 = 0 0 + t = 6.244997998 + 3 t = 6.244997998 + 3 Combine like terms: 6.244997998 + 3 = 9.244997998 t = 9.244997998 Simplifying t = 9.244997998Subproblem 2
t + -3 = -6.244997998 Simplifying t + -3 = -6.244997998 Reorder the terms: -3 + t = -6.244997998 Solving -3 + t = -6.244997998 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 = -6.244997998 + 3 Combine like terms: -3 + 3 = 0 0 + t = -6.244997998 + 3 t = -6.244997998 + 3 Combine like terms: -6.244997998 + 3 = -3.244997998 t = -3.244997998 Simplifying t = -3.244997998Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.244997998, -3.244997998}Solution
t = {9.244997998, -3.244997998}
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