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Simplifying 0 = 2 + 300t + -16t2 Solving 0 = 2 + 300t + -16t2 Solving for variable 't'. Combine like terms: 0 + -2 = -2 -2 + -300t + 16t2 = 2 + 300t + -16t2 + -2 + -300t + 16t2 Reorder the terms: -2 + -300t + 16t2 = 2 + -2 + 300t + -300t + -16t2 + 16t2 Combine like terms: 2 + -2 = 0 -2 + -300t + 16t2 = 0 + 300t + -300t + -16t2 + 16t2 -2 + -300t + 16t2 = 300t + -300t + -16t2 + 16t2 Combine like terms: 300t + -300t = 0 -2 + -300t + 16t2 = 0 + -16t2 + 16t2 -2 + -300t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -2 + -300t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + -150t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -150t + 8t2)' equal to zero and attempt to solve: Simplifying -1 + -150t + 8t2 = 0 Solving -1 + -150t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.125 + -18.75t + t2 = 0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + -18.75t + 0.125 + t2 = 0 + 0.125 Reorder the terms: -0.125 + 0.125 + -18.75t + t2 = 0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + -18.75t + t2 = 0 + 0.125 -18.75t + t2 = 0 + 0.125 Combine like terms: 0 + 0.125 = 0.125 -18.75t + t2 = 0.125 The t term is -18.75t. Take half its coefficient (-9.375). Square it (87.890625) and add it to both sides. Add '87.890625' to each side of the equation. -18.75t + 87.890625 + t2 = 0.125 + 87.890625 Reorder the terms: 87.890625 + -18.75t + t2 = 0.125 + 87.890625 Combine like terms: 0.125 + 87.890625 = 88.015625 87.890625 + -18.75t + t2 = 88.015625 Factor a perfect square on the left side: (t + -9.375)(t + -9.375) = 88.015625 Calculate the square root of the right side: 9.381664298 Break this problem into two subproblems by setting (t + -9.375) equal to 9.381664298 and -9.381664298.Subproblem 1
t + -9.375 = 9.381664298 Simplifying t + -9.375 = 9.381664298 Reorder the terms: -9.375 + t = 9.381664298 Solving -9.375 + t = 9.381664298 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '9.375' to each side of the equation. -9.375 + 9.375 + t = 9.381664298 + 9.375 Combine like terms: -9.375 + 9.375 = 0.000 0.000 + t = 9.381664298 + 9.375 t = 9.381664298 + 9.375 Combine like terms: 9.381664298 + 9.375 = 18.756664298 t = 18.756664298 Simplifying t = 18.756664298Subproblem 2
t + -9.375 = -9.381664298 Simplifying t + -9.375 = -9.381664298 Reorder the terms: -9.375 + t = -9.381664298 Solving -9.375 + t = -9.381664298 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '9.375' to each side of the equation. -9.375 + 9.375 + t = -9.381664298 + 9.375 Combine like terms: -9.375 + 9.375 = 0.000 0.000 + t = -9.381664298 + 9.375 t = -9.381664298 + 9.375 Combine like terms: -9.381664298 + 9.375 = -0.006664298 t = -0.006664298 Simplifying t = -0.006664298Solution
The solution to the problem is based on the solutions from the subproblems. t = {18.756664298, -0.006664298}Solution
t = {18.756664298, -0.006664298}
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