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Simplifying 0 = -16t2 + 99t + 122 Reorder the terms: 0 = 122 + 99t + -16t2 Solving 0 = 122 + 99t + -16t2 Solving for variable 't'. Combine like terms: 0 + -122 = -122 -122 + -99t + 16t2 = 122 + 99t + -16t2 + -122 + -99t + 16t2 Reorder the terms: -122 + -99t + 16t2 = 122 + -122 + 99t + -99t + -16t2 + 16t2 Combine like terms: 122 + -122 = 0 -122 + -99t + 16t2 = 0 + 99t + -99t + -16t2 + 16t2 -122 + -99t + 16t2 = 99t + -99t + -16t2 + 16t2 Combine like terms: 99t + -99t = 0 -122 + -99t + 16t2 = 0 + -16t2 + 16t2 -122 + -99t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -122 + -99t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -7.625 + -6.1875t + t2 = 0 Move the constant term to the right: Add '7.625' to each side of the equation. -7.625 + -6.1875t + 7.625 + t2 = 0 + 7.625 Reorder the terms: -7.625 + 7.625 + -6.1875t + t2 = 0 + 7.625 Combine like terms: -7.625 + 7.625 = 0.000 0.000 + -6.1875t + t2 = 0 + 7.625 -6.1875t + t2 = 0 + 7.625 Combine like terms: 0 + 7.625 = 7.625 -6.1875t + t2 = 7.625 The t term is -6.1875t. Take half its coefficient (-3.09375). Square it (9.571289063) and add it to both sides. Add '9.571289063' to each side of the equation. -6.1875t + 9.571289063 + t2 = 7.625 + 9.571289063 Reorder the terms: 9.571289063 + -6.1875t + t2 = 7.625 + 9.571289063 Combine like terms: 7.625 + 9.571289063 = 17.196289063 9.571289063 + -6.1875t + t2 = 17.196289063 Factor a perfect square on the left side: (t + -3.09375)(t + -3.09375) = 17.196289063 Calculate the square root of the right side: 4.146840853 Break this problem into two subproblems by setting (t + -3.09375) equal to 4.146840853 and -4.146840853.Subproblem 1
t + -3.09375 = 4.146840853 Simplifying t + -3.09375 = 4.146840853 Reorder the terms: -3.09375 + t = 4.146840853 Solving -3.09375 + t = 4.146840853 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.09375' to each side of the equation. -3.09375 + 3.09375 + t = 4.146840853 + 3.09375 Combine like terms: -3.09375 + 3.09375 = 0.00000 0.00000 + t = 4.146840853 + 3.09375 t = 4.146840853 + 3.09375 Combine like terms: 4.146840853 + 3.09375 = 7.240590853 t = 7.240590853 Simplifying t = 7.240590853Subproblem 2
t + -3.09375 = -4.146840853 Simplifying t + -3.09375 = -4.146840853 Reorder the terms: -3.09375 + t = -4.146840853 Solving -3.09375 + t = -4.146840853 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.09375' to each side of the equation. -3.09375 + 3.09375 + t = -4.146840853 + 3.09375 Combine like terms: -3.09375 + 3.09375 = 0.00000 0.00000 + t = -4.146840853 + 3.09375 t = -4.146840853 + 3.09375 Combine like terms: -4.146840853 + 3.09375 = -1.053090853 t = -1.053090853 Simplifying t = -1.053090853Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.240590853, -1.053090853}
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