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Simplifying 141 = 16t2 + 32t Reorder the terms: 141 = 32t + 16t2 Solving 141 = 32t + 16t2 Solving for variable 't'. Reorder the terms: 141 + -32t + -16t2 = 32t + -32t + 16t2 + -16t2 Combine like terms: 32t + -32t = 0 141 + -32t + -16t2 = 0 + 16t2 + -16t2 141 + -32t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 141 + -32t + -16t2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -8.8125 + 2t + t2 = 0 Move the constant term to the right: Add '8.8125' to each side of the equation. -8.8125 + 2t + 8.8125 + t2 = 0 + 8.8125 Reorder the terms: -8.8125 + 8.8125 + 2t + t2 = 0 + 8.8125 Combine like terms: -8.8125 + 8.8125 = 0.0000 0.0000 + 2t + t2 = 0 + 8.8125 2t + t2 = 0 + 8.8125 Combine like terms: 0 + 8.8125 = 8.8125 2t + t2 = 8.8125 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 = 8.8125 + 1 Reorder the terms: 1 + 2t + t2 = 8.8125 + 1 Combine like terms: 8.8125 + 1 = 9.8125 1 + 2t + t2 = 9.8125 Factor a perfect square on the left side: (t + 1)(t + 1) = 9.8125 Calculate the square root of the right side: 3.132491022 Break this problem into two subproblems by setting (t + 1) equal to 3.132491022 and -3.132491022.Subproblem 1
t + 1 = 3.132491022 Simplifying t + 1 = 3.132491022 Reorder the terms: 1 + t = 3.132491022 Solving 1 + t = 3.132491022 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 = 3.132491022 + -1 Combine like terms: 1 + -1 = 0 0 + t = 3.132491022 + -1 t = 3.132491022 + -1 Combine like terms: 3.132491022 + -1 = 2.132491022 t = 2.132491022 Simplifying t = 2.132491022Subproblem 2
t + 1 = -3.132491022 Simplifying t + 1 = -3.132491022 Reorder the terms: 1 + t = -3.132491022 Solving 1 + t = -3.132491022 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 = -3.132491022 + -1 Combine like terms: 1 + -1 = 0 0 + t = -3.132491022 + -1 t = -3.132491022 + -1 Combine like terms: -3.132491022 + -1 = -4.132491022 t = -4.132491022 Simplifying t = -4.132491022Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.132491022, -4.132491022}
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