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Simplifying 98t + -16t2 + -49 = 0 Reorder the terms: -49 + 98t + -16t2 = 0 Solving -49 + 98t + -16t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. 3.0625 + -6.125t + t2 = 0 Move the constant term to the right: Add '-3.0625' to each side of the equation. 3.0625 + -6.125t + -3.0625 + t2 = 0 + -3.0625 Reorder the terms: 3.0625 + -3.0625 + -6.125t + t2 = 0 + -3.0625 Combine like terms: 3.0625 + -3.0625 = 0.0000 0.0000 + -6.125t + t2 = 0 + -3.0625 -6.125t + t2 = 0 + -3.0625 Combine like terms: 0 + -3.0625 = -3.0625 -6.125t + t2 = -3.0625 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 = -3.0625 + 9.37890625 Reorder the terms: 9.37890625 + -6.125t + t2 = -3.0625 + 9.37890625 Combine like terms: -3.0625 + 9.37890625 = 6.31640625 9.37890625 + -6.125t + t2 = 6.31640625 Factor a perfect square on the left side: (t + -3.0625)(t + -3.0625) = 6.31640625 Calculate the square root of the right side: 2.513246158 Break this problem into two subproblems by setting (t + -3.0625) equal to 2.513246158 and -2.513246158.Subproblem 1
t + -3.0625 = 2.513246158 Simplifying t + -3.0625 = 2.513246158 Reorder the terms: -3.0625 + t = 2.513246158 Solving -3.0625 + t = 2.513246158 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 = 2.513246158 + 3.0625 Combine like terms: -3.0625 + 3.0625 = 0.0000 0.0000 + t = 2.513246158 + 3.0625 t = 2.513246158 + 3.0625 Combine like terms: 2.513246158 + 3.0625 = 5.575746158 t = 5.575746158 Simplifying t = 5.575746158Subproblem 2
t + -3.0625 = -2.513246158 Simplifying t + -3.0625 = -2.513246158 Reorder the terms: -3.0625 + t = -2.513246158 Solving -3.0625 + t = -2.513246158 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 = -2.513246158 + 3.0625 Combine like terms: -3.0625 + 3.0625 = 0.0000 0.0000 + t = -2.513246158 + 3.0625 t = -2.513246158 + 3.0625 Combine like terms: -2.513246158 + 3.0625 = 0.549253842 t = 0.549253842 Simplifying t = 0.549253842Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.575746158, 0.549253842}
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