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Simplifying 3t2 + -24t + 40 = 0 Reorder the terms: 40 + -24t + 3t2 = 0 Solving 40 + -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'. 13.33333333 + -8t + t2 = 0 Move the constant term to the right: Add '-13.33333333' to each side of the equation. 13.33333333 + -8t + -13.33333333 + t2 = 0 + -13.33333333 Reorder the terms: 13.33333333 + -13.33333333 + -8t + t2 = 0 + -13.33333333 Combine like terms: 13.33333333 + -13.33333333 = 0.00000000 0.00000000 + -8t + t2 = 0 + -13.33333333 -8t + t2 = 0 + -13.33333333 Combine like terms: 0 + -13.33333333 = -13.33333333 -8t + t2 = -13.33333333 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 = -13.33333333 + 16 Reorder the terms: 16 + -8t + t2 = -13.33333333 + 16 Combine like terms: -13.33333333 + 16 = 2.66666667 16 + -8t + t2 = 2.66666667 Factor a perfect square on the left side: (t + -4)(t + -4) = 2.66666667 Calculate the square root of the right side: 1.632993163 Break this problem into two subproblems by setting (t + -4) equal to 1.632993163 and -1.632993163.Subproblem 1
t + -4 = 1.632993163 Simplifying t + -4 = 1.632993163 Reorder the terms: -4 + t = 1.632993163 Solving -4 + t = 1.632993163 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 = 1.632993163 + 4 Combine like terms: -4 + 4 = 0 0 + t = 1.632993163 + 4 t = 1.632993163 + 4 Combine like terms: 1.632993163 + 4 = 5.632993163 t = 5.632993163 Simplifying t = 5.632993163Subproblem 2
t + -4 = -1.632993163 Simplifying t + -4 = -1.632993163 Reorder the terms: -4 + t = -1.632993163 Solving -4 + t = -1.632993163 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 = -1.632993163 + 4 Combine like terms: -4 + 4 = 0 0 + t = -1.632993163 + 4 t = -1.632993163 + 4 Combine like terms: -1.632993163 + 4 = 2.367006837 t = 2.367006837 Simplifying t = 2.367006837Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.632993163, 2.367006837}
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