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Simplifying 0 = -16t2 + 104t + -98 Reorder the terms: 0 = -98 + 104t + -16t2 Solving 0 = -98 + 104t + -16t2 Solving for variable 't'. Combine like terms: 0 + 98 = 98 98 + -104t + 16t2 = -98 + 104t + -16t2 + 98 + -104t + 16t2 Reorder the terms: 98 + -104t + 16t2 = -98 + 98 + 104t + -104t + -16t2 + 16t2 Combine like terms: -98 + 98 = 0 98 + -104t + 16t2 = 0 + 104t + -104t + -16t2 + 16t2 98 + -104t + 16t2 = 104t + -104t + -16t2 + 16t2 Combine like terms: 104t + -104t = 0 98 + -104t + 16t2 = 0 + -16t2 + 16t2 98 + -104t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 98 + -104t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(49 + -52t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(49 + -52t + 8t2)' equal to zero and attempt to solve: Simplifying 49 + -52t + 8t2 = 0 Solving 49 + -52t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 6.125 + -6.5t + t2 = 0 Move the constant term to the right: Add '-6.125' to each side of the equation. 6.125 + -6.5t + -6.125 + t2 = 0 + -6.125 Reorder the terms: 6.125 + -6.125 + -6.5t + t2 = 0 + -6.125 Combine like terms: 6.125 + -6.125 = 0.000 0.000 + -6.5t + t2 = 0 + -6.125 -6.5t + t2 = 0 + -6.125 Combine like terms: 0 + -6.125 = -6.125 -6.5t + t2 = -6.125 The t term is -6.5t. Take half its coefficient (-3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. -6.5t + 10.5625 + t2 = -6.125 + 10.5625 Reorder the terms: 10.5625 + -6.5t + t2 = -6.125 + 10.5625 Combine like terms: -6.125 + 10.5625 = 4.4375 10.5625 + -6.5t + t2 = 4.4375 Factor a perfect square on the left side: (t + -3.25)(t + -3.25) = 4.4375 Calculate the square root of the right side: 2.106537443 Break this problem into two subproblems by setting (t + -3.25) equal to 2.106537443 and -2.106537443.Subproblem 1
t + -3.25 = 2.106537443 Simplifying t + -3.25 = 2.106537443 Reorder the terms: -3.25 + t = 2.106537443 Solving -3.25 + t = 2.106537443 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + t = 2.106537443 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + t = 2.106537443 + 3.25 t = 2.106537443 + 3.25 Combine like terms: 2.106537443 + 3.25 = 5.356537443 t = 5.356537443 Simplifying t = 5.356537443Subproblem 2
t + -3.25 = -2.106537443 Simplifying t + -3.25 = -2.106537443 Reorder the terms: -3.25 + t = -2.106537443 Solving -3.25 + t = -2.106537443 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + t = -2.106537443 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + t = -2.106537443 + 3.25 t = -2.106537443 + 3.25 Combine like terms: -2.106537443 + 3.25 = 1.143462557 t = 1.143462557 Simplifying t = 1.143462557Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.356537443, 1.143462557}Solution
t = {5.356537443, 1.143462557}
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