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Simplifying 3t2 + -21t + 29 = 0 Reorder the terms: 29 + -21t + 3t2 = 0 Solving 29 + -21t + 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'. 9.666666667 + -7t + t2 = 0 Move the constant term to the right: Add '-9.666666667' to each side of the equation. 9.666666667 + -7t + -9.666666667 + t2 = 0 + -9.666666667 Reorder the terms: 9.666666667 + -9.666666667 + -7t + t2 = 0 + -9.666666667 Combine like terms: 9.666666667 + -9.666666667 = 0.000000000 0.000000000 + -7t + t2 = 0 + -9.666666667 -7t + t2 = 0 + -9.666666667 Combine like terms: 0 + -9.666666667 = -9.666666667 -7t + t2 = -9.666666667 The t term is -7t. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7t + 12.25 + t2 = -9.666666667 + 12.25 Reorder the terms: 12.25 + -7t + t2 = -9.666666667 + 12.25 Combine like terms: -9.666666667 + 12.25 = 2.583333333 12.25 + -7t + t2 = 2.583333333 Factor a perfect square on the left side: (t + -3.5)(t + -3.5) = 2.583333333 Calculate the square root of the right side: 1.607275127 Break this problem into two subproblems by setting (t + -3.5) equal to 1.607275127 and -1.607275127.Subproblem 1
t + -3.5 = 1.607275127 Simplifying t + -3.5 = 1.607275127 Reorder the terms: -3.5 + t = 1.607275127 Solving -3.5 + t = 1.607275127 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + t = 1.607275127 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + t = 1.607275127 + 3.5 t = 1.607275127 + 3.5 Combine like terms: 1.607275127 + 3.5 = 5.107275127 t = 5.107275127 Simplifying t = 5.107275127Subproblem 2
t + -3.5 = -1.607275127 Simplifying t + -3.5 = -1.607275127 Reorder the terms: -3.5 + t = -1.607275127 Solving -3.5 + t = -1.607275127 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + t = -1.607275127 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + t = -1.607275127 + 3.5 t = -1.607275127 + 3.5 Combine like terms: -1.607275127 + 3.5 = 1.892724873 t = 1.892724873 Simplifying t = 1.892724873Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.107275127, 1.892724873}
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