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Simplifying 3t2 + 24t + 1 = 0 Reorder the terms: 1 + 24t + 3t2 = 0 Solving 1 + 24t + 3t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.3333333333 + 8t + t2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + 8t + -0.3333333333 + t2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + 8t + t2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + 8t + t2 = 0 + -0.3333333333 8t + t2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 8t + t2 = -0.3333333333 The t term is 8t. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8t + 16 + t2 = -0.3333333333 + 16 Reorder the terms: 16 + 8t + t2 = -0.3333333333 + 16 Combine like terms: -0.3333333333 + 16 = 15.6666666667 16 + 8t + t2 = 15.6666666667 Factor a perfect square on the left side: (t + 4)(t + 4) = 15.6666666667 Calculate the square root of the right side: 3.958114029 Break this problem into two subproblems by setting (t + 4) equal to 3.958114029 and -3.958114029.Subproblem 1
t + 4 = 3.958114029 Simplifying t + 4 = 3.958114029 Reorder the terms: 4 + t = 3.958114029 Solving 4 + t = 3.958114029 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + t = 3.958114029 + -4 Combine like terms: 4 + -4 = 0 0 + t = 3.958114029 + -4 t = 3.958114029 + -4 Combine like terms: 3.958114029 + -4 = -0.041885971 t = -0.041885971 Simplifying t = -0.041885971Subproblem 2
t + 4 = -3.958114029 Simplifying t + 4 = -3.958114029 Reorder the terms: 4 + t = -3.958114029 Solving 4 + t = -3.958114029 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + t = -3.958114029 + -4 Combine like terms: 4 + -4 = 0 0 + t = -3.958114029 + -4 t = -3.958114029 + -4 Combine like terms: -3.958114029 + -4 = -7.958114029 t = -7.958114029 Simplifying t = -7.958114029Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.041885971, -7.958114029}
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