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Simplifying 0 = 16t2 + 96t + 4 Reorder the terms: 0 = 4 + 96t + 16t2 Solving 0 = 4 + 96t + 16t2 Solving for variable 't'. Combine like terms: 0 + -4 = -4 -4 + -96t + -16t2 = 4 + 96t + 16t2 + -4 + -96t + -16t2 Reorder the terms: -4 + -96t + -16t2 = 4 + -4 + 96t + -96t + 16t2 + -16t2 Combine like terms: 4 + -4 = 0 -4 + -96t + -16t2 = 0 + 96t + -96t + 16t2 + -16t2 -4 + -96t + -16t2 = 96t + -96t + 16t2 + -16t2 Combine like terms: 96t + -96t = 0 -4 + -96t + -16t2 = 0 + 16t2 + -16t2 -4 + -96t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 -4 + -96t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '-4'. -4(1 + 24t + 4t2) = 0 Ignore the factor -4.Subproblem 1
Set the factor '(1 + 24t + 4t2)' equal to zero and attempt to solve: Simplifying 1 + 24t + 4t2 = 0 Solving 1 + 24t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.25 + 6t + t2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + 6t + -0.25 + t2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + 6t + t2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + 6t + t2 = 0 + -0.25 6t + t2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 6t + t2 = -0.25 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 = -0.25 + 9 Reorder the terms: 9 + 6t + t2 = -0.25 + 9 Combine like terms: -0.25 + 9 = 8.75 9 + 6t + t2 = 8.75 Factor a perfect square on the left side: (t + 3)(t + 3) = 8.75 Calculate the square root of the right side: 2.958039892 Break this problem into two subproblems by setting (t + 3) equal to 2.958039892 and -2.958039892.Subproblem 1
t + 3 = 2.958039892 Simplifying t + 3 = 2.958039892 Reorder the terms: 3 + t = 2.958039892 Solving 3 + t = 2.958039892 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 = 2.958039892 + -3 Combine like terms: 3 + -3 = 0 0 + t = 2.958039892 + -3 t = 2.958039892 + -3 Combine like terms: 2.958039892 + -3 = -0.041960108 t = -0.041960108 Simplifying t = -0.041960108Subproblem 2
t + 3 = -2.958039892 Simplifying t + 3 = -2.958039892 Reorder the terms: 3 + t = -2.958039892 Solving 3 + t = -2.958039892 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 = -2.958039892 + -3 Combine like terms: 3 + -3 = 0 0 + t = -2.958039892 + -3 t = -2.958039892 + -3 Combine like terms: -2.958039892 + -3 = -5.958039892 t = -5.958039892 Simplifying t = -5.958039892Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.041960108, -5.958039892}Solution
t = {-0.041960108, -5.958039892}
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