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Simplifying t2 + -10t + -1000 = 0 Reorder the terms: -1000 + -10t + t2 = 0 Solving -1000 + -10t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '1000' to each side of the equation. -1000 + -10t + 1000 + t2 = 0 + 1000 Reorder the terms: -1000 + 1000 + -10t + t2 = 0 + 1000 Combine like terms: -1000 + 1000 = 0 0 + -10t + t2 = 0 + 1000 -10t + t2 = 0 + 1000 Combine like terms: 0 + 1000 = 1000 -10t + t2 = 1000 The t term is -10t. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10t + 25 + t2 = 1000 + 25 Reorder the terms: 25 + -10t + t2 = 1000 + 25 Combine like terms: 1000 + 25 = 1025 25 + -10t + t2 = 1025 Factor a perfect square on the left side: (t + -5)(t + -5) = 1025 Calculate the square root of the right side: 32.015621187 Break this problem into two subproblems by setting (t + -5) equal to 32.015621187 and -32.015621187.Subproblem 1
t + -5 = 32.015621187 Simplifying t + -5 = 32.015621187 Reorder the terms: -5 + t = 32.015621187 Solving -5 + t = 32.015621187 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + t = 32.015621187 + 5 Combine like terms: -5 + 5 = 0 0 + t = 32.015621187 + 5 t = 32.015621187 + 5 Combine like terms: 32.015621187 + 5 = 37.015621187 t = 37.015621187 Simplifying t = 37.015621187Subproblem 2
t + -5 = -32.015621187 Simplifying t + -5 = -32.015621187 Reorder the terms: -5 + t = -32.015621187 Solving -5 + t = -32.015621187 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + t = -32.015621187 + 5 Combine like terms: -5 + 5 = 0 0 + t = -32.015621187 + 5 t = -32.015621187 + 5 Combine like terms: -32.015621187 + 5 = -27.015621187 t = -27.015621187 Simplifying t = -27.015621187Solution
The solution to the problem is based on the solutions from the subproblems. t = {37.015621187, -27.015621187}
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