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Simplifying 3t2 + -6t = 123 Reorder the terms: -6t + 3t2 = 123 Solving -6t + 3t2 = 123 Solving for variable 't'. Reorder the terms: -123 + -6t + 3t2 = 123 + -123 Combine like terms: 123 + -123 = 0 -123 + -6t + 3t2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-41 + -2t + t2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-41 + -2t + t2)' equal to zero and attempt to solve: Simplifying -41 + -2t + t2 = 0 Solving -41 + -2t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '41' to each side of the equation. -41 + -2t + 41 + t2 = 0 + 41 Reorder the terms: -41 + 41 + -2t + t2 = 0 + 41 Combine like terms: -41 + 41 = 0 0 + -2t + t2 = 0 + 41 -2t + t2 = 0 + 41 Combine like terms: 0 + 41 = 41 -2t + t2 = 41 The t term is -2t. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2t + 1 + t2 = 41 + 1 Reorder the terms: 1 + -2t + t2 = 41 + 1 Combine like terms: 41 + 1 = 42 1 + -2t + t2 = 42 Factor a perfect square on the left side: (t + -1)(t + -1) = 42 Calculate the square root of the right side: 6.480740698 Break this problem into two subproblems by setting (t + -1) equal to 6.480740698 and -6.480740698.Subproblem 1
t + -1 = 6.480740698 Simplifying t + -1 = 6.480740698 Reorder the terms: -1 + t = 6.480740698 Solving -1 + t = 6.480740698 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + t = 6.480740698 + 1 Combine like terms: -1 + 1 = 0 0 + t = 6.480740698 + 1 t = 6.480740698 + 1 Combine like terms: 6.480740698 + 1 = 7.480740698 t = 7.480740698 Simplifying t = 7.480740698Subproblem 2
t + -1 = -6.480740698 Simplifying t + -1 = -6.480740698 Reorder the terms: -1 + t = -6.480740698 Solving -1 + t = -6.480740698 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + t = -6.480740698 + 1 Combine like terms: -1 + 1 = 0 0 + t = -6.480740698 + 1 t = -6.480740698 + 1 Combine like terms: -6.480740698 + 1 = -5.480740698 t = -5.480740698 Simplifying t = -5.480740698Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.480740698, -5.480740698}Solution
t = {7.480740698, -5.480740698}
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