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Simplifying 0 = 4000 + -55t + -1t2 Solving 0 = 4000 + -55t + -1t2 Solving for variable 't'. Combine like terms: 0 + -4000 = -4000 -4000 + 55t + t2 = 4000 + -55t + -1t2 + -4000 + 55t + t2 Reorder the terms: -4000 + 55t + t2 = 4000 + -4000 + -55t + 55t + -1t2 + t2 Combine like terms: 4000 + -4000 = 0 -4000 + 55t + t2 = 0 + -55t + 55t + -1t2 + t2 -4000 + 55t + t2 = -55t + 55t + -1t2 + t2 Combine like terms: -55t + 55t = 0 -4000 + 55t + t2 = 0 + -1t2 + t2 -4000 + 55t + t2 = -1t2 + t2 Combine like terms: -1t2 + t2 = 0 -4000 + 55t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '4000' to each side of the equation. -4000 + 55t + 4000 + t2 = 0 + 4000 Reorder the terms: -4000 + 4000 + 55t + t2 = 0 + 4000 Combine like terms: -4000 + 4000 = 0 0 + 55t + t2 = 0 + 4000 55t + t2 = 0 + 4000 Combine like terms: 0 + 4000 = 4000 55t + t2 = 4000 The t term is 55t. Take half its coefficient (27.5). Square it (756.25) and add it to both sides. Add '756.25' to each side of the equation. 55t + 756.25 + t2 = 4000 + 756.25 Reorder the terms: 756.25 + 55t + t2 = 4000 + 756.25 Combine like terms: 4000 + 756.25 = 4756.25 756.25 + 55t + t2 = 4756.25 Factor a perfect square on the left side: (t + 27.5)(t + 27.5) = 4756.25 Calculate the square root of the right side: 68.965571121 Break this problem into two subproblems by setting (t + 27.5) equal to 68.965571121 and -68.965571121.Subproblem 1
t + 27.5 = 68.965571121 Simplifying t + 27.5 = 68.965571121 Reorder the terms: 27.5 + t = 68.965571121 Solving 27.5 + t = 68.965571121 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-27.5' to each side of the equation. 27.5 + -27.5 + t = 68.965571121 + -27.5 Combine like terms: 27.5 + -27.5 = 0.0 0.0 + t = 68.965571121 + -27.5 t = 68.965571121 + -27.5 Combine like terms: 68.965571121 + -27.5 = 41.465571121 t = 41.465571121 Simplifying t = 41.465571121Subproblem 2
t + 27.5 = -68.965571121 Simplifying t + 27.5 = -68.965571121 Reorder the terms: 27.5 + t = -68.965571121 Solving 27.5 + t = -68.965571121 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-27.5' to each side of the equation. 27.5 + -27.5 + t = -68.965571121 + -27.5 Combine like terms: 27.5 + -27.5 = 0.0 0.0 + t = -68.965571121 + -27.5 t = -68.965571121 + -27.5 Combine like terms: -68.965571121 + -27.5 = -96.465571121 t = -96.465571121 Simplifying t = -96.465571121Solution
The solution to the problem is based on the solutions from the subproblems. t = {41.465571121, -96.465571121}
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