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Simplifying 200t2 + 3600t + -6400 = 8500 Reorder the terms: -6400 + 3600t + 200t2 = 8500 Solving -6400 + 3600t + 200t2 = 8500 Solving for variable 't'. Reorder the terms: -6400 + -8500 + 3600t + 200t2 = 8500 + -8500 Combine like terms: -6400 + -8500 = -14900 -14900 + 3600t + 200t2 = 8500 + -8500 Combine like terms: 8500 + -8500 = 0 -14900 + 3600t + 200t2 = 0 Factor out the Greatest Common Factor (GCF), '100'. 100(-149 + 36t + 2t2) = 0 Ignore the factor 100.Subproblem 1
Set the factor '(-149 + 36t + 2t2)' equal to zero and attempt to solve: Simplifying -149 + 36t + 2t2 = 0 Solving -149 + 36t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -74.5 + 18t + t2 = 0 Move the constant term to the right: Add '74.5' to each side of the equation. -74.5 + 18t + 74.5 + t2 = 0 + 74.5 Reorder the terms: -74.5 + 74.5 + 18t + t2 = 0 + 74.5 Combine like terms: -74.5 + 74.5 = 0.0 0.0 + 18t + t2 = 0 + 74.5 18t + t2 = 0 + 74.5 Combine like terms: 0 + 74.5 = 74.5 18t + t2 = 74.5 The t term is 18t. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18t + 81 + t2 = 74.5 + 81 Reorder the terms: 81 + 18t + t2 = 74.5 + 81 Combine like terms: 74.5 + 81 = 155.5 81 + 18t + t2 = 155.5 Factor a perfect square on the left side: (t + 9)(t + 9) = 155.5 Calculate the square root of the right side: 12.469963913 Break this problem into two subproblems by setting (t + 9) equal to 12.469963913 and -12.469963913.Subproblem 1
t + 9 = 12.469963913 Simplifying t + 9 = 12.469963913 Reorder the terms: 9 + t = 12.469963913 Solving 9 + t = 12.469963913 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + t = 12.469963913 + -9 Combine like terms: 9 + -9 = 0 0 + t = 12.469963913 + -9 t = 12.469963913 + -9 Combine like terms: 12.469963913 + -9 = 3.469963913 t = 3.469963913 Simplifying t = 3.469963913Subproblem 2
t + 9 = -12.469963913 Simplifying t + 9 = -12.469963913 Reorder the terms: 9 + t = -12.469963913 Solving 9 + t = -12.469963913 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + t = -12.469963913 + -9 Combine like terms: 9 + -9 = 0 0 + t = -12.469963913 + -9 t = -12.469963913 + -9 Combine like terms: -12.469963913 + -9 = -21.469963913 t = -21.469963913 Simplifying t = -21.469963913Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.469963913, -21.469963913}Solution
t = {3.469963913, -21.469963913}
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