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Simplifying -16t2 + 96t + -107 = 0 Reorder the terms: -107 + 96t + -16t2 = 0 Solving -107 + 96t + -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'. 6.6875 + -6t + t2 = 0 Move the constant term to the right: Add '-6.6875' to each side of the equation. 6.6875 + -6t + -6.6875 + t2 = 0 + -6.6875 Reorder the terms: 6.6875 + -6.6875 + -6t + t2 = 0 + -6.6875 Combine like terms: 6.6875 + -6.6875 = 0.0000 0.0000 + -6t + t2 = 0 + -6.6875 -6t + t2 = 0 + -6.6875 Combine like terms: 0 + -6.6875 = -6.6875 -6t + t2 = -6.6875 The t term is -6t. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6t + 9 + t2 = -6.6875 + 9 Reorder the terms: 9 + -6t + t2 = -6.6875 + 9 Combine like terms: -6.6875 + 9 = 2.3125 9 + -6t + t2 = 2.3125 Factor a perfect square on the left side: (t + -3)(t + -3) = 2.3125 Calculate the square root of the right side: 1.520690633 Break this problem into two subproblems by setting (t + -3) equal to 1.520690633 and -1.520690633.Subproblem 1
t + -3 = 1.520690633 Simplifying t + -3 = 1.520690633 Reorder the terms: -3 + t = 1.520690633 Solving -3 + t = 1.520690633 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = 1.520690633 + 3 Combine like terms: -3 + 3 = 0 0 + t = 1.520690633 + 3 t = 1.520690633 + 3 Combine like terms: 1.520690633 + 3 = 4.520690633 t = 4.520690633 Simplifying t = 4.520690633Subproblem 2
t + -3 = -1.520690633 Simplifying t + -3 = -1.520690633 Reorder the terms: -3 + t = -1.520690633 Solving -3 + t = -1.520690633 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = -1.520690633 + 3 Combine like terms: -3 + 3 = 0 0 + t = -1.520690633 + 3 t = -1.520690633 + 3 Combine like terms: -1.520690633 + 3 = 1.479309367 t = 1.479309367 Simplifying t = 1.479309367Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.520690633, 1.479309367}
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