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Simplifying 0 = 16t2 + 340t + 3 Reorder the terms: 0 = 3 + 340t + 16t2 Solving 0 = 3 + 340t + 16t2 Solving for variable 't'. Combine like terms: 0 + -3 = -3 -3 + -340t + -16t2 = 3 + 340t + 16t2 + -3 + -340t + -16t2 Reorder the terms: -3 + -340t + -16t2 = 3 + -3 + 340t + -340t + 16t2 + -16t2 Combine like terms: 3 + -3 = 0 -3 + -340t + -16t2 = 0 + 340t + -340t + 16t2 + -16t2 -3 + -340t + -16t2 = 340t + -340t + 16t2 + -16t2 Combine like terms: 340t + -340t = 0 -3 + -340t + -16t2 = 0 + 16t2 + -16t2 -3 + -340t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 -3 + -340t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(3 + 340t + 16t2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(3 + 340t + 16t2)' equal to zero and attempt to solve: Simplifying 3 + 340t + 16t2 = 0 Solving 3 + 340t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.1875 + 21.25t + t2 = 0 Move the constant term to the right: Add '-0.1875' to each side of the equation. 0.1875 + 21.25t + -0.1875 + t2 = 0 + -0.1875 Reorder the terms: 0.1875 + -0.1875 + 21.25t + t2 = 0 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + 21.25t + t2 = 0 + -0.1875 21.25t + t2 = 0 + -0.1875 Combine like terms: 0 + -0.1875 = -0.1875 21.25t + t2 = -0.1875 The t term is 21.25t. Take half its coefficient (10.625). Square it (112.890625) and add it to both sides. Add '112.890625' to each side of the equation. 21.25t + 112.890625 + t2 = -0.1875 + 112.890625 Reorder the terms: 112.890625 + 21.25t + t2 = -0.1875 + 112.890625 Combine like terms: -0.1875 + 112.890625 = 112.703125 112.890625 + 21.25t + t2 = 112.703125 Factor a perfect square on the left side: (t + 10.625)(t + 10.625) = 112.703125 Calculate the square root of the right side: 10.616172804 Break this problem into two subproblems by setting (t + 10.625) equal to 10.616172804 and -10.616172804.Subproblem 1
t + 10.625 = 10.616172804 Simplifying t + 10.625 = 10.616172804 Reorder the terms: 10.625 + t = 10.616172804 Solving 10.625 + t = 10.616172804 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-10.625' to each side of the equation. 10.625 + -10.625 + t = 10.616172804 + -10.625 Combine like terms: 10.625 + -10.625 = 0.000 0.000 + t = 10.616172804 + -10.625 t = 10.616172804 + -10.625 Combine like terms: 10.616172804 + -10.625 = -0.008827196 t = -0.008827196 Simplifying t = -0.008827196Subproblem 2
t + 10.625 = -10.616172804 Simplifying t + 10.625 = -10.616172804 Reorder the terms: 10.625 + t = -10.616172804 Solving 10.625 + t = -10.616172804 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-10.625' to each side of the equation. 10.625 + -10.625 + t = -10.616172804 + -10.625 Combine like terms: 10.625 + -10.625 = 0.000 0.000 + t = -10.616172804 + -10.625 t = -10.616172804 + -10.625 Combine like terms: -10.616172804 + -10.625 = -21.241172804 t = -21.241172804 Simplifying t = -21.241172804Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.008827196, -21.241172804}Solution
t = {-0.008827196, -21.241172804}
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