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Simplifying 36 + -24t + 3t2 = 5 Solving 36 + -24t + 3t2 = 5 Solving for variable 't'. Reorder the terms: 36 + -5 + -24t + 3t2 = 5 + -5 Combine like terms: 36 + -5 = 31 31 + -24t + 3t2 = 5 + -5 Combine like terms: 5 + -5 = 0 31 + -24t + 3t2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 10.33333333 + -8t + t2 = 0 Move the constant term to the right: Add '-10.33333333' to each side of the equation. 10.33333333 + -8t + -10.33333333 + t2 = 0 + -10.33333333 Reorder the terms: 10.33333333 + -10.33333333 + -8t + t2 = 0 + -10.33333333 Combine like terms: 10.33333333 + -10.33333333 = 0.00000000 0.00000000 + -8t + t2 = 0 + -10.33333333 -8t + t2 = 0 + -10.33333333 Combine like terms: 0 + -10.33333333 = -10.33333333 -8t + t2 = -10.33333333 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 = -10.33333333 + 16 Reorder the terms: 16 + -8t + t2 = -10.33333333 + 16 Combine like terms: -10.33333333 + 16 = 5.66666667 16 + -8t + t2 = 5.66666667 Factor a perfect square on the left side: (t + -4)(t + -4) = 5.66666667 Calculate the square root of the right side: 2.380476144 Break this problem into two subproblems by setting (t + -4) equal to 2.380476144 and -2.380476144.Subproblem 1
t + -4 = 2.380476144 Simplifying t + -4 = 2.380476144 Reorder the terms: -4 + t = 2.380476144 Solving -4 + t = 2.380476144 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 = 2.380476144 + 4 Combine like terms: -4 + 4 = 0 0 + t = 2.380476144 + 4 t = 2.380476144 + 4 Combine like terms: 2.380476144 + 4 = 6.380476144 t = 6.380476144 Simplifying t = 6.380476144Subproblem 2
t + -4 = -2.380476144 Simplifying t + -4 = -2.380476144 Reorder the terms: -4 + t = -2.380476144 Solving -4 + t = -2.380476144 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 = -2.380476144 + 4 Combine like terms: -4 + 4 = 0 0 + t = -2.380476144 + 4 t = -2.380476144 + 4 Combine like terms: -2.380476144 + 4 = 1.619523856 t = 1.619523856 Simplifying t = 1.619523856Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.380476144, 1.619523856}
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