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Simplifying 0 = -16t2 + 45t + 6 Reorder the terms: 0 = 6 + 45t + -16t2 Solving 0 = 6 + 45t + -16t2 Solving for variable 't'. Combine like terms: 0 + -6 = -6 -6 + -45t + 16t2 = 6 + 45t + -16t2 + -6 + -45t + 16t2 Reorder the terms: -6 + -45t + 16t2 = 6 + -6 + 45t + -45t + -16t2 + 16t2 Combine like terms: 6 + -6 = 0 -6 + -45t + 16t2 = 0 + 45t + -45t + -16t2 + 16t2 -6 + -45t + 16t2 = 45t + -45t + -16t2 + 16t2 Combine like terms: 45t + -45t = 0 -6 + -45t + 16t2 = 0 + -16t2 + 16t2 -6 + -45t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -6 + -45t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.375 + -2.8125t + t2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + -2.8125t + 0.375 + t2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + -2.8125t + t2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + -2.8125t + t2 = 0 + 0.375 -2.8125t + t2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 -2.8125t + t2 = 0.375 The t term is -2.8125t. Take half its coefficient (-1.40625). Square it (1.977539063) and add it to both sides. Add '1.977539063' to each side of the equation. -2.8125t + 1.977539063 + t2 = 0.375 + 1.977539063 Reorder the terms: 1.977539063 + -2.8125t + t2 = 0.375 + 1.977539063 Combine like terms: 0.375 + 1.977539063 = 2.352539063 1.977539063 + -2.8125t + t2 = 2.352539063 Factor a perfect square on the left side: (t + -1.40625)(t + -1.40625) = 2.352539063 Calculate the square root of the right side: 1.533798899 Break this problem into two subproblems by setting (t + -1.40625) equal to 1.533798899 and -1.533798899.Subproblem 1
t + -1.40625 = 1.533798899 Simplifying t + -1.40625 = 1.533798899 Reorder the terms: -1.40625 + t = 1.533798899 Solving -1.40625 + t = 1.533798899 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.40625' to each side of the equation. -1.40625 + 1.40625 + t = 1.533798899 + 1.40625 Combine like terms: -1.40625 + 1.40625 = 0.00000 0.00000 + t = 1.533798899 + 1.40625 t = 1.533798899 + 1.40625 Combine like terms: 1.533798899 + 1.40625 = 2.940048899 t = 2.940048899 Simplifying t = 2.940048899Subproblem 2
t + -1.40625 = -1.533798899 Simplifying t + -1.40625 = -1.533798899 Reorder the terms: -1.40625 + t = -1.533798899 Solving -1.40625 + t = -1.533798899 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.40625' to each side of the equation. -1.40625 + 1.40625 + t = -1.533798899 + 1.40625 Combine like terms: -1.40625 + 1.40625 = 0.00000 0.00000 + t = -1.533798899 + 1.40625 t = -1.533798899 + 1.40625 Combine like terms: -1.533798899 + 1.40625 = -0.127548899 t = -0.127548899 Simplifying t = -0.127548899Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.940048899, -0.127548899}
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