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Simplifying t2 + -271t + 5085 = 0 Reorder the terms: 5085 + -271t + t2 = 0 Solving 5085 + -271t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '-5085' to each side of the equation. 5085 + -271t + -5085 + t2 = 0 + -5085 Reorder the terms: 5085 + -5085 + -271t + t2 = 0 + -5085 Combine like terms: 5085 + -5085 = 0 0 + -271t + t2 = 0 + -5085 -271t + t2 = 0 + -5085 Combine like terms: 0 + -5085 = -5085 -271t + t2 = -5085 The t term is -271t. Take half its coefficient (-135.5). Square it (18360.25) and add it to both sides. Add '18360.25' to each side of the equation. -271t + 18360.25 + t2 = -5085 + 18360.25 Reorder the terms: 18360.25 + -271t + t2 = -5085 + 18360.25 Combine like terms: -5085 + 18360.25 = 13275.25 18360.25 + -271t + t2 = 13275.25 Factor a perfect square on the left side: (t + -135.5)(t + -135.5) = 13275.25 Calculate the square root of the right side: 115.218271121 Break this problem into two subproblems by setting (t + -135.5) equal to 115.218271121 and -115.218271121.Subproblem 1
t + -135.5 = 115.218271121 Simplifying t + -135.5 = 115.218271121 Reorder the terms: -135.5 + t = 115.218271121 Solving -135.5 + t = 115.218271121 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '135.5' to each side of the equation. -135.5 + 135.5 + t = 115.218271121 + 135.5 Combine like terms: -135.5 + 135.5 = 0.0 0.0 + t = 115.218271121 + 135.5 t = 115.218271121 + 135.5 Combine like terms: 115.218271121 + 135.5 = 250.718271121 t = 250.718271121 Simplifying t = 250.718271121Subproblem 2
t + -135.5 = -115.218271121 Simplifying t + -135.5 = -115.218271121 Reorder the terms: -135.5 + t = -115.218271121 Solving -135.5 + t = -115.218271121 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '135.5' to each side of the equation. -135.5 + 135.5 + t = -115.218271121 + 135.5 Combine like terms: -135.5 + 135.5 = 0.0 0.0 + t = -115.218271121 + 135.5 t = -115.218271121 + 135.5 Combine like terms: -115.218271121 + 135.5 = 20.281728879 t = 20.281728879 Simplifying t = 20.281728879Solution
The solution to the problem is based on the solutions from the subproblems. t = {250.718271121, 20.281728879}
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