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Simplifying 0 = -16t2 + 113t + -106 Reorder the terms: 0 = -106 + 113t + -16t2 Solving 0 = -106 + 113t + -16t2 Solving for variable 't'. Combine like terms: 0 + 106 = 106 106 + -113t + 16t2 = -106 + 113t + -16t2 + 106 + -113t + 16t2 Reorder the terms: 106 + -113t + 16t2 = -106 + 106 + 113t + -113t + -16t2 + 16t2 Combine like terms: -106 + 106 = 0 106 + -113t + 16t2 = 0 + 113t + -113t + -16t2 + 16t2 106 + -113t + 16t2 = 113t + -113t + -16t2 + 16t2 Combine like terms: 113t + -113t = 0 106 + -113t + 16t2 = 0 + -16t2 + 16t2 106 + -113t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 106 + -113t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 6.625 + -7.0625t + t2 = 0 Move the constant term to the right: Add '-6.625' to each side of the equation. 6.625 + -7.0625t + -6.625 + t2 = 0 + -6.625 Reorder the terms: 6.625 + -6.625 + -7.0625t + t2 = 0 + -6.625 Combine like terms: 6.625 + -6.625 = 0.000 0.000 + -7.0625t + t2 = 0 + -6.625 -7.0625t + t2 = 0 + -6.625 Combine like terms: 0 + -6.625 = -6.625 -7.0625t + t2 = -6.625 The t term is -7.0625t. Take half its coefficient (-3.53125). Square it (12.46972656) and add it to both sides. Add '12.46972656' to each side of the equation. -7.0625t + 12.46972656 + t2 = -6.625 + 12.46972656 Reorder the terms: 12.46972656 + -7.0625t + t2 = -6.625 + 12.46972656 Combine like terms: -6.625 + 12.46972656 = 5.84472656 12.46972656 + -7.0625t + t2 = 5.84472656 Factor a perfect square on the left side: (t + -3.53125)(t + -3.53125) = 5.84472656 Calculate the square root of the right side: 2.417586929 Break this problem into two subproblems by setting (t + -3.53125) equal to 2.417586929 and -2.417586929.Subproblem 1
t + -3.53125 = 2.417586929 Simplifying t + -3.53125 = 2.417586929 Reorder the terms: -3.53125 + t = 2.417586929 Solving -3.53125 + t = 2.417586929 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.53125' to each side of the equation. -3.53125 + 3.53125 + t = 2.417586929 + 3.53125 Combine like terms: -3.53125 + 3.53125 = 0.00000 0.00000 + t = 2.417586929 + 3.53125 t = 2.417586929 + 3.53125 Combine like terms: 2.417586929 + 3.53125 = 5.948836929 t = 5.948836929 Simplifying t = 5.948836929Subproblem 2
t + -3.53125 = -2.417586929 Simplifying t + -3.53125 = -2.417586929 Reorder the terms: -3.53125 + t = -2.417586929 Solving -3.53125 + t = -2.417586929 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.53125' to each side of the equation. -3.53125 + 3.53125 + t = -2.417586929 + 3.53125 Combine like terms: -3.53125 + 3.53125 = 0.00000 0.00000 + t = -2.417586929 + 3.53125 t = -2.417586929 + 3.53125 Combine like terms: -2.417586929 + 3.53125 = 1.113663071 t = 1.113663071 Simplifying t = 1.113663071Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.948836929, 1.113663071}
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