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Simplifying 60 = -16t2 + -12t + 500 Reorder the terms: 60 = 500 + -12t + -16t2 Solving 60 = 500 + -12t + -16t2 Solving for variable 't'. Combine like terms: 60 + -500 = -440 -440 + 12t + 16t2 = 500 + -12t + -16t2 + -500 + 12t + 16t2 Reorder the terms: -440 + 12t + 16t2 = 500 + -500 + -12t + 12t + -16t2 + 16t2 Combine like terms: 500 + -500 = 0 -440 + 12t + 16t2 = 0 + -12t + 12t + -16t2 + 16t2 -440 + 12t + 16t2 = -12t + 12t + -16t2 + 16t2 Combine like terms: -12t + 12t = 0 -440 + 12t + 16t2 = 0 + -16t2 + 16t2 -440 + 12t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -440 + 12t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-110 + 3t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-110 + 3t + 4t2)' equal to zero and attempt to solve: Simplifying -110 + 3t + 4t2 = 0 Solving -110 + 3t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -27.5 + 0.75t + t2 = 0 Move the constant term to the right: Add '27.5' to each side of the equation. -27.5 + 0.75t + 27.5 + t2 = 0 + 27.5 Reorder the terms: -27.5 + 27.5 + 0.75t + t2 = 0 + 27.5 Combine like terms: -27.5 + 27.5 = 0.0 0.0 + 0.75t + t2 = 0 + 27.5 0.75t + t2 = 0 + 27.5 Combine like terms: 0 + 27.5 = 27.5 0.75t + t2 = 27.5 The t term is 0.75t. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75t + 0.140625 + t2 = 27.5 + 0.140625 Reorder the terms: 0.140625 + 0.75t + t2 = 27.5 + 0.140625 Combine like terms: 27.5 + 0.140625 = 27.640625 0.140625 + 0.75t + t2 = 27.640625 Factor a perfect square on the left side: (t + 0.375)(t + 0.375) = 27.640625 Calculate the square root of the right side: 5.257435211 Break this problem into two subproblems by setting (t + 0.375) equal to 5.257435211 and -5.257435211.Subproblem 1
t + 0.375 = 5.257435211 Simplifying t + 0.375 = 5.257435211 Reorder the terms: 0.375 + t = 5.257435211 Solving 0.375 + t = 5.257435211 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + t = 5.257435211 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + t = 5.257435211 + -0.375 t = 5.257435211 + -0.375 Combine like terms: 5.257435211 + -0.375 = 4.882435211 t = 4.882435211 Simplifying t = 4.882435211Subproblem 2
t + 0.375 = -5.257435211 Simplifying t + 0.375 = -5.257435211 Reorder the terms: 0.375 + t = -5.257435211 Solving 0.375 + t = -5.257435211 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + t = -5.257435211 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + t = -5.257435211 + -0.375 t = -5.257435211 + -0.375 Combine like terms: -5.257435211 + -0.375 = -5.632435211 t = -5.632435211 Simplifying t = -5.632435211Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.882435211, -5.632435211}Solution
t = {4.882435211, -5.632435211}
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