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Simplifying 0 = -16t2 + 98t + 211 Reorder the terms: 0 = 211 + 98t + -16t2 Solving 0 = 211 + 98t + -16t2 Solving for variable 't'. Combine like terms: 0 + -211 = -211 -211 + -98t + 16t2 = 211 + 98t + -16t2 + -211 + -98t + 16t2 Reorder the terms: -211 + -98t + 16t2 = 211 + -211 + 98t + -98t + -16t2 + 16t2 Combine like terms: 211 + -211 = 0 -211 + -98t + 16t2 = 0 + 98t + -98t + -16t2 + 16t2 -211 + -98t + 16t2 = 98t + -98t + -16t2 + 16t2 Combine like terms: 98t + -98t = 0 -211 + -98t + 16t2 = 0 + -16t2 + 16t2 -211 + -98t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -211 + -98t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -13.1875 + -6.125t + t2 = 0 Move the constant term to the right: Add '13.1875' to each side of the equation. -13.1875 + -6.125t + 13.1875 + t2 = 0 + 13.1875 Reorder the terms: -13.1875 + 13.1875 + -6.125t + t2 = 0 + 13.1875 Combine like terms: -13.1875 + 13.1875 = 0.0000 0.0000 + -6.125t + t2 = 0 + 13.1875 -6.125t + t2 = 0 + 13.1875 Combine like terms: 0 + 13.1875 = 13.1875 -6.125t + t2 = 13.1875 The t term is -6.125t. Take half its coefficient (-3.0625). Square it (9.37890625) and add it to both sides. Add '9.37890625' to each side of the equation. -6.125t + 9.37890625 + t2 = 13.1875 + 9.37890625 Reorder the terms: 9.37890625 + -6.125t + t2 = 13.1875 + 9.37890625 Combine like terms: 13.1875 + 9.37890625 = 22.56640625 9.37890625 + -6.125t + t2 = 22.56640625 Factor a perfect square on the left side: (t + -3.0625)(t + -3.0625) = 22.56640625 Calculate the square root of the right side: 4.750411166 Break this problem into two subproblems by setting (t + -3.0625) equal to 4.750411166 and -4.750411166.Subproblem 1
t + -3.0625 = 4.750411166 Simplifying t + -3.0625 = 4.750411166 Reorder the terms: -3.0625 + t = 4.750411166 Solving -3.0625 + t = 4.750411166 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.0625' to each side of the equation. -3.0625 + 3.0625 + t = 4.750411166 + 3.0625 Combine like terms: -3.0625 + 3.0625 = 0.0000 0.0000 + t = 4.750411166 + 3.0625 t = 4.750411166 + 3.0625 Combine like terms: 4.750411166 + 3.0625 = 7.812911166 t = 7.812911166 Simplifying t = 7.812911166Subproblem 2
t + -3.0625 = -4.750411166 Simplifying t + -3.0625 = -4.750411166 Reorder the terms: -3.0625 + t = -4.750411166 Solving -3.0625 + t = -4.750411166 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.0625' to each side of the equation. -3.0625 + 3.0625 + t = -4.750411166 + 3.0625 Combine like terms: -3.0625 + 3.0625 = 0.0000 0.0000 + t = -4.750411166 + 3.0625 t = -4.750411166 + 3.0625 Combine like terms: -4.750411166 + 3.0625 = -1.687911166 t = -1.687911166 Simplifying t = -1.687911166Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.812911166, -1.687911166}
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