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Simplifying 77t = 77 + -16t2 Solving 77t = 77 + -16t2 Solving for variable 't'. Reorder the terms: -77 + 77t + 16t2 = 77 + -16t2 + -77 + 16t2 Reorder the terms: -77 + 77t + 16t2 = 77 + -77 + -16t2 + 16t2 Combine like terms: 77 + -77 = 0 -77 + 77t + 16t2 = 0 + -16t2 + 16t2 -77 + 77t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -77 + 77t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -4.8125 + 4.8125t + t2 = 0 Move the constant term to the right: Add '4.8125' to each side of the equation. -4.8125 + 4.8125t + 4.8125 + t2 = 0 + 4.8125 Reorder the terms: -4.8125 + 4.8125 + 4.8125t + t2 = 0 + 4.8125 Combine like terms: -4.8125 + 4.8125 = 0.0000 0.0000 + 4.8125t + t2 = 0 + 4.8125 4.8125t + t2 = 0 + 4.8125 Combine like terms: 0 + 4.8125 = 4.8125 4.8125t + t2 = 4.8125 The t term is 4.8125t. Take half its coefficient (2.40625). Square it (5.790039063) and add it to both sides. Add '5.790039063' to each side of the equation. 4.8125t + 5.790039063 + t2 = 4.8125 + 5.790039063 Reorder the terms: 5.790039063 + 4.8125t + t2 = 4.8125 + 5.790039063 Combine like terms: 4.8125 + 5.790039063 = 10.602539063 5.790039063 + 4.8125t + t2 = 10.602539063 Factor a perfect square on the left side: (t + 2.40625)(t + 2.40625) = 10.602539063 Calculate the square root of the right side: 3.256154029 Break this problem into two subproblems by setting (t + 2.40625) equal to 3.256154029 and -3.256154029.Subproblem 1
t + 2.40625 = 3.256154029 Simplifying t + 2.40625 = 3.256154029 Reorder the terms: 2.40625 + t = 3.256154029 Solving 2.40625 + t = 3.256154029 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.40625' to each side of the equation. 2.40625 + -2.40625 + t = 3.256154029 + -2.40625 Combine like terms: 2.40625 + -2.40625 = 0.00000 0.00000 + t = 3.256154029 + -2.40625 t = 3.256154029 + -2.40625 Combine like terms: 3.256154029 + -2.40625 = 0.849904029 t = 0.849904029 Simplifying t = 0.849904029Subproblem 2
t + 2.40625 = -3.256154029 Simplifying t + 2.40625 = -3.256154029 Reorder the terms: 2.40625 + t = -3.256154029 Solving 2.40625 + t = -3.256154029 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.40625' to each side of the equation. 2.40625 + -2.40625 + t = -3.256154029 + -2.40625 Combine like terms: 2.40625 + -2.40625 = 0.00000 0.00000 + t = -3.256154029 + -2.40625 t = -3.256154029 + -2.40625 Combine like terms: -3.256154029 + -2.40625 = -5.662404029 t = -5.662404029 Simplifying t = -5.662404029Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.849904029, -5.662404029}
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