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Simplifying 0 = -16t2 + 159t + -349 Reorder the terms: 0 = -349 + 159t + -16t2 Solving 0 = -349 + 159t + -16t2 Solving for variable 't'. Combine like terms: 0 + 349 = 349 349 + -159t + 16t2 = -349 + 159t + -16t2 + 349 + -159t + 16t2 Reorder the terms: 349 + -159t + 16t2 = -349 + 349 + 159t + -159t + -16t2 + 16t2 Combine like terms: -349 + 349 = 0 349 + -159t + 16t2 = 0 + 159t + -159t + -16t2 + 16t2 349 + -159t + 16t2 = 159t + -159t + -16t2 + 16t2 Combine like terms: 159t + -159t = 0 349 + -159t + 16t2 = 0 + -16t2 + 16t2 349 + -159t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 349 + -159t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 21.8125 + -9.9375t + t2 = 0 Move the constant term to the right: Add '-21.8125' to each side of the equation. 21.8125 + -9.9375t + -21.8125 + t2 = 0 + -21.8125 Reorder the terms: 21.8125 + -21.8125 + -9.9375t + t2 = 0 + -21.8125 Combine like terms: 21.8125 + -21.8125 = 0.0000 0.0000 + -9.9375t + t2 = 0 + -21.8125 -9.9375t + t2 = 0 + -21.8125 Combine like terms: 0 + -21.8125 = -21.8125 -9.9375t + t2 = -21.8125 The t term is -9.9375t. Take half its coefficient (-4.96875). Square it (24.68847656) and add it to both sides. Add '24.68847656' to each side of the equation. -9.9375t + 24.68847656 + t2 = -21.8125 + 24.68847656 Reorder the terms: 24.68847656 + -9.9375t + t2 = -21.8125 + 24.68847656 Combine like terms: -21.8125 + 24.68847656 = 2.87597656 24.68847656 + -9.9375t + t2 = 2.87597656 Factor a perfect square on the left side: (t + -4.96875)(t + -4.96875) = 2.87597656 Calculate the square root of the right side: 1.695870443 Break this problem into two subproblems by setting (t + -4.96875) equal to 1.695870443 and -1.695870443.Subproblem 1
t + -4.96875 = 1.695870443 Simplifying t + -4.96875 = 1.695870443 Reorder the terms: -4.96875 + t = 1.695870443 Solving -4.96875 + t = 1.695870443 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.96875' to each side of the equation. -4.96875 + 4.96875 + t = 1.695870443 + 4.96875 Combine like terms: -4.96875 + 4.96875 = 0.00000 0.00000 + t = 1.695870443 + 4.96875 t = 1.695870443 + 4.96875 Combine like terms: 1.695870443 + 4.96875 = 6.664620443 t = 6.664620443 Simplifying t = 6.664620443Subproblem 2
t + -4.96875 = -1.695870443 Simplifying t + -4.96875 = -1.695870443 Reorder the terms: -4.96875 + t = -1.695870443 Solving -4.96875 + t = -1.695870443 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.96875' to each side of the equation. -4.96875 + 4.96875 + t = -1.695870443 + 4.96875 Combine like terms: -4.96875 + 4.96875 = 0.00000 0.00000 + t = -1.695870443 + 4.96875 t = -1.695870443 + 4.96875 Combine like terms: -1.695870443 + 4.96875 = 3.272879557 t = 3.272879557 Simplifying t = 3.272879557Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.664620443, 3.272879557}
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