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Simplifying 40 = 64t + -16t2 Solving 40 = 64t + -16t2 Solving for variable 't'. Reorder the terms: 40 + -64t + 16t2 = 64t + -64t + -16t2 + 16t2 Combine like terms: 64t + -64t = 0 40 + -64t + 16t2 = 0 + -16t2 + 16t2 40 + -64t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 40 + -64t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(5 + -8t + 2t2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(5 + -8t + 2t2)' equal to zero and attempt to solve: Simplifying 5 + -8t + 2t2 = 0 Solving 5 + -8t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2.5 + -4t + t2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + -4t + -2.5 + t2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + -4t + t2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -4t + t2 = 0 + -2.5 -4t + t2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 -4t + t2 = -2.5 The t term is -4t. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4t + 4 + t2 = -2.5 + 4 Reorder the terms: 4 + -4t + t2 = -2.5 + 4 Combine like terms: -2.5 + 4 = 1.5 4 + -4t + t2 = 1.5 Factor a perfect square on the left side: (t + -2)(t + -2) = 1.5 Calculate the square root of the right side: 1.224744871 Break this problem into two subproblems by setting (t + -2) equal to 1.224744871 and -1.224744871.Subproblem 1
t + -2 = 1.224744871 Simplifying t + -2 = 1.224744871 Reorder the terms: -2 + t = 1.224744871 Solving -2 + t = 1.224744871 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = 1.224744871 + 2 Combine like terms: -2 + 2 = 0 0 + t = 1.224744871 + 2 t = 1.224744871 + 2 Combine like terms: 1.224744871 + 2 = 3.224744871 t = 3.224744871 Simplifying t = 3.224744871Subproblem 2
t + -2 = -1.224744871 Simplifying t + -2 = -1.224744871 Reorder the terms: -2 + t = -1.224744871 Solving -2 + t = -1.224744871 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = -1.224744871 + 2 Combine like terms: -2 + 2 = 0 0 + t = -1.224744871 + 2 t = -1.224744871 + 2 Combine like terms: -1.224744871 + 2 = 0.775255129 t = 0.775255129 Simplifying t = 0.775255129Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.224744871, 0.775255129}Solution
t = {3.224744871, 0.775255129}
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