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Simplifying 16t2 + 40t = 555 Reorder the terms: 40t + 16t2 = 555 Solving 40t + 16t2 = 555 Solving for variable 't'. Reorder the terms: -555 + 40t + 16t2 = 555 + -555 Combine like terms: 555 + -555 = 0 -555 + 40t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -34.6875 + 2.5t + t2 = 0 Move the constant term to the right: Add '34.6875' to each side of the equation. -34.6875 + 2.5t + 34.6875 + t2 = 0 + 34.6875 Reorder the terms: -34.6875 + 34.6875 + 2.5t + t2 = 0 + 34.6875 Combine like terms: -34.6875 + 34.6875 = 0.0000 0.0000 + 2.5t + t2 = 0 + 34.6875 2.5t + t2 = 0 + 34.6875 Combine like terms: 0 + 34.6875 = 34.6875 2.5t + t2 = 34.6875 The t term is 2.5t. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5t + 1.5625 + t2 = 34.6875 + 1.5625 Reorder the terms: 1.5625 + 2.5t + t2 = 34.6875 + 1.5625 Combine like terms: 34.6875 + 1.5625 = 36.25 1.5625 + 2.5t + t2 = 36.25 Factor a perfect square on the left side: (t + 1.25)(t + 1.25) = 36.25 Calculate the square root of the right side: 6.020797289 Break this problem into two subproblems by setting (t + 1.25) equal to 6.020797289 and -6.020797289.Subproblem 1
t + 1.25 = 6.020797289 Simplifying t + 1.25 = 6.020797289 Reorder the terms: 1.25 + t = 6.020797289 Solving 1.25 + t = 6.020797289 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + t = 6.020797289 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + t = 6.020797289 + -1.25 t = 6.020797289 + -1.25 Combine like terms: 6.020797289 + -1.25 = 4.770797289 t = 4.770797289 Simplifying t = 4.770797289Subproblem 2
t + 1.25 = -6.020797289 Simplifying t + 1.25 = -6.020797289 Reorder the terms: 1.25 + t = -6.020797289 Solving 1.25 + t = -6.020797289 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + t = -6.020797289 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + t = -6.020797289 + -1.25 t = -6.020797289 + -1.25 Combine like terms: -6.020797289 + -1.25 = -7.270797289 t = -7.270797289 Simplifying t = -7.270797289Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.770797289, -7.270797289}
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