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Simplifying 0 = 16t2 + 120t + -150 Reorder the terms: 0 = -150 + 120t + 16t2 Solving 0 = -150 + 120t + 16t2 Solving for variable 't'. Combine like terms: 0 + 150 = 150 150 + -120t + -16t2 = -150 + 120t + 16t2 + 150 + -120t + -16t2 Reorder the terms: 150 + -120t + -16t2 = -150 + 150 + 120t + -120t + 16t2 + -16t2 Combine like terms: -150 + 150 = 0 150 + -120t + -16t2 = 0 + 120t + -120t + 16t2 + -16t2 150 + -120t + -16t2 = 120t + -120t + 16t2 + -16t2 Combine like terms: 120t + -120t = 0 150 + -120t + -16t2 = 0 + 16t2 + -16t2 150 + -120t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 150 + -120t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(75 + -60t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(75 + -60t + -8t2)' equal to zero and attempt to solve: Simplifying 75 + -60t + -8t2 = 0 Solving 75 + -60t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -9.375 + 7.5t + t2 = 0 Move the constant term to the right: Add '9.375' to each side of the equation. -9.375 + 7.5t + 9.375 + t2 = 0 + 9.375 Reorder the terms: -9.375 + 9.375 + 7.5t + t2 = 0 + 9.375 Combine like terms: -9.375 + 9.375 = 0.000 0.000 + 7.5t + t2 = 0 + 9.375 7.5t + t2 = 0 + 9.375 Combine like terms: 0 + 9.375 = 9.375 7.5t + t2 = 9.375 The t term is 7.5t. Take half its coefficient (3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. 7.5t + 14.0625 + t2 = 9.375 + 14.0625 Reorder the terms: 14.0625 + 7.5t + t2 = 9.375 + 14.0625 Combine like terms: 9.375 + 14.0625 = 23.4375 14.0625 + 7.5t + t2 = 23.4375 Factor a perfect square on the left side: (t + 3.75)(t + 3.75) = 23.4375 Calculate the square root of the right side: 4.841229183 Break this problem into two subproblems by setting (t + 3.75) equal to 4.841229183 and -4.841229183.Subproblem 1
t + 3.75 = 4.841229183 Simplifying t + 3.75 = 4.841229183 Reorder the terms: 3.75 + t = 4.841229183 Solving 3.75 + t = 4.841229183 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + t = 4.841229183 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + t = 4.841229183 + -3.75 t = 4.841229183 + -3.75 Combine like terms: 4.841229183 + -3.75 = 1.091229183 t = 1.091229183 Simplifying t = 1.091229183Subproblem 2
t + 3.75 = -4.841229183 Simplifying t + 3.75 = -4.841229183 Reorder the terms: 3.75 + t = -4.841229183 Solving 3.75 + t = -4.841229183 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + t = -4.841229183 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + t = -4.841229183 + -3.75 t = -4.841229183 + -3.75 Combine like terms: -4.841229183 + -3.75 = -8.591229183 t = -8.591229183 Simplifying t = -8.591229183Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.091229183, -8.591229183}Solution
t = {1.091229183, -8.591229183}
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