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Simplifying 10 = -16t2 + -96t Reorder the terms: 10 = -96t + -16t2 Solving 10 = -96t + -16t2 Solving for variable 't'. Reorder the terms: 10 + 96t + 16t2 = -96t + 96t + -16t2 + 16t2 Combine like terms: -96t + 96t = 0 10 + 96t + 16t2 = 0 + -16t2 + 16t2 10 + 96t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 10 + 96t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(5 + 48t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + 48t + 8t2)' equal to zero and attempt to solve: Simplifying 5 + 48t + 8t2 = 0 Solving 5 + 48t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.625 + 6t + t2 = 0 Move the constant term to the right: Add '-0.625' to each side of the equation. 0.625 + 6t + -0.625 + t2 = 0 + -0.625 Reorder the terms: 0.625 + -0.625 + 6t + t2 = 0 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + 6t + t2 = 0 + -0.625 6t + t2 = 0 + -0.625 Combine like terms: 0 + -0.625 = -0.625 6t + t2 = -0.625 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 = -0.625 + 9 Reorder the terms: 9 + 6t + t2 = -0.625 + 9 Combine like terms: -0.625 + 9 = 8.375 9 + 6t + t2 = 8.375 Factor a perfect square on the left side: (t + 3)(t + 3) = 8.375 Calculate the square root of the right side: 2.893959226 Break this problem into two subproblems by setting (t + 3) equal to 2.893959226 and -2.893959226.Subproblem 1
t + 3 = 2.893959226 Simplifying t + 3 = 2.893959226 Reorder the terms: 3 + t = 2.893959226 Solving 3 + t = 2.893959226 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 = 2.893959226 + -3 Combine like terms: 3 + -3 = 0 0 + t = 2.893959226 + -3 t = 2.893959226 + -3 Combine like terms: 2.893959226 + -3 = -0.106040774 t = -0.106040774 Simplifying t = -0.106040774Subproblem 2
t + 3 = -2.893959226 Simplifying t + 3 = -2.893959226 Reorder the terms: 3 + t = -2.893959226 Solving 3 + t = -2.893959226 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 = -2.893959226 + -3 Combine like terms: 3 + -3 = 0 0 + t = -2.893959226 + -3 t = -2.893959226 + -3 Combine like terms: -2.893959226 + -3 = -5.893959226 t = -5.893959226 Simplifying t = -5.893959226Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.106040774, -5.893959226}Solution
t = {-0.106040774, -5.893959226}
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