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Simplifying 0 = 16t2 + 120t + 4 Reorder the terms: 0 = 4 + 120t + 16t2 Solving 0 = 4 + 120t + 16t2 Solving for variable 't'. Combine like terms: 0 + -4 = -4 -4 + -120t + -16t2 = 4 + 120t + 16t2 + -4 + -120t + -16t2 Reorder the terms: -4 + -120t + -16t2 = 4 + -4 + 120t + -120t + 16t2 + -16t2 Combine like terms: 4 + -4 = 0 -4 + -120t + -16t2 = 0 + 120t + -120t + 16t2 + -16t2 -4 + -120t + -16t2 = 120t + -120t + 16t2 + -16t2 Combine like terms: 120t + -120t = 0 -4 + -120t + -16t2 = 0 + 16t2 + -16t2 -4 + -120t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 -4 + -120t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '-4'. -4(1 + 30t + 4t2) = 0 Ignore the factor -4.Subproblem 1
Set the factor '(1 + 30t + 4t2)' equal to zero and attempt to solve: Simplifying 1 + 30t + 4t2 = 0 Solving 1 + 30t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.25 + 7.5t + t2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + 7.5t + -0.25 + t2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + 7.5t + t2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + 7.5t + t2 = 0 + -0.25 7.5t + t2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 7.5t + t2 = -0.25 The t term is 7.5t. Take half its coefficient (3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. 7.5t + 14.0625 + t2 = -0.25 + 14.0625 Reorder the terms: 14.0625 + 7.5t + t2 = -0.25 + 14.0625 Combine like terms: -0.25 + 14.0625 = 13.8125 14.0625 + 7.5t + t2 = 13.8125 Factor a perfect square on the left side: (t + 3.75)(t + 3.75) = 13.8125 Calculate the square root of the right side: 3.716517187 Break this problem into two subproblems by setting (t + 3.75) equal to 3.716517187 and -3.716517187.Subproblem 1
t + 3.75 = 3.716517187 Simplifying t + 3.75 = 3.716517187 Reorder the terms: 3.75 + t = 3.716517187 Solving 3.75 + t = 3.716517187 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + t = 3.716517187 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + t = 3.716517187 + -3.75 t = 3.716517187 + -3.75 Combine like terms: 3.716517187 + -3.75 = -0.033482813 t = -0.033482813 Simplifying t = -0.033482813Subproblem 2
t + 3.75 = -3.716517187 Simplifying t + 3.75 = -3.716517187 Reorder the terms: 3.75 + t = -3.716517187 Solving 3.75 + t = -3.716517187 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + t = -3.716517187 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + t = -3.716517187 + -3.75 t = -3.716517187 + -3.75 Combine like terms: -3.716517187 + -3.75 = -7.466517187 t = -7.466517187 Simplifying t = -7.466517187Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.033482813, -7.466517187}Solution
t = {-0.033482813, -7.466517187}
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