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Simplifying 16t2 + 175t + 60 = 0 Reorder the terms: 60 + 175t + 16t2 = 0 Solving 60 + 175t + 16t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 3.75 + 10.9375t + t2 = 0 Move the constant term to the right: Add '-3.75' to each side of the equation. 3.75 + 10.9375t + -3.75 + t2 = 0 + -3.75 Reorder the terms: 3.75 + -3.75 + 10.9375t + t2 = 0 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + 10.9375t + t2 = 0 + -3.75 10.9375t + t2 = 0 + -3.75 Combine like terms: 0 + -3.75 = -3.75 10.9375t + t2 = -3.75 The t term is 10.9375t. Take half its coefficient (5.46875). Square it (29.90722656) and add it to both sides. Add '29.90722656' to each side of the equation. 10.9375t + 29.90722656 + t2 = -3.75 + 29.90722656 Reorder the terms: 29.90722656 + 10.9375t + t2 = -3.75 + 29.90722656 Combine like terms: -3.75 + 29.90722656 = 26.15722656 29.90722656 + 10.9375t + t2 = 26.15722656 Factor a perfect square on the left side: (t + 5.46875)(t + 5.46875) = 26.15722656 Calculate the square root of the right side: 5.114413609 Break this problem into two subproblems by setting (t + 5.46875) equal to 5.114413609 and -5.114413609.Subproblem 1
t + 5.46875 = 5.114413609 Simplifying t + 5.46875 = 5.114413609 Reorder the terms: 5.46875 + t = 5.114413609 Solving 5.46875 + t = 5.114413609 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-5.46875' to each side of the equation. 5.46875 + -5.46875 + t = 5.114413609 + -5.46875 Combine like terms: 5.46875 + -5.46875 = 0.00000 0.00000 + t = 5.114413609 + -5.46875 t = 5.114413609 + -5.46875 Combine like terms: 5.114413609 + -5.46875 = -0.354336391 t = -0.354336391 Simplifying t = -0.354336391Subproblem 2
t + 5.46875 = -5.114413609 Simplifying t + 5.46875 = -5.114413609 Reorder the terms: 5.46875 + t = -5.114413609 Solving 5.46875 + t = -5.114413609 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-5.46875' to each side of the equation. 5.46875 + -5.46875 + t = -5.114413609 + -5.46875 Combine like terms: 5.46875 + -5.46875 = 0.00000 0.00000 + t = -5.114413609 + -5.46875 t = -5.114413609 + -5.46875 Combine like terms: -5.114413609 + -5.46875 = -10.583163609 t = -10.583163609 Simplifying t = -10.583163609Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.354336391, -10.583163609}
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