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Simplifying t2 + -66t + 1 = 0 Reorder the terms: 1 + -66t + t2 = 0 Solving 1 + -66t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -66t + -1 + t2 = 0 + -1 Reorder the terms: 1 + -1 + -66t + t2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -66t + t2 = 0 + -1 -66t + t2 = 0 + -1 Combine like terms: 0 + -1 = -1 -66t + t2 = -1 The t term is -66t. Take half its coefficient (-33). Square it (1089) and add it to both sides. Add '1089' to each side of the equation. -66t + 1089 + t2 = -1 + 1089 Reorder the terms: 1089 + -66t + t2 = -1 + 1089 Combine like terms: -1 + 1089 = 1088 1089 + -66t + t2 = 1088 Factor a perfect square on the left side: (t + -33)(t + -33) = 1088 Calculate the square root of the right side: 32.984845005 Break this problem into two subproblems by setting (t + -33) equal to 32.984845005 and -32.984845005.Subproblem 1
t + -33 = 32.984845005 Simplifying t + -33 = 32.984845005 Reorder the terms: -33 + t = 32.984845005 Solving -33 + t = 32.984845005 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '33' to each side of the equation. -33 + 33 + t = 32.984845005 + 33 Combine like terms: -33 + 33 = 0 0 + t = 32.984845005 + 33 t = 32.984845005 + 33 Combine like terms: 32.984845005 + 33 = 65.984845005 t = 65.984845005 Simplifying t = 65.984845005Subproblem 2
t + -33 = -32.984845005 Simplifying t + -33 = -32.984845005 Reorder the terms: -33 + t = -32.984845005 Solving -33 + t = -32.984845005 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '33' to each side of the equation. -33 + 33 + t = -32.984845005 + 33 Combine like terms: -33 + 33 = 0 0 + t = -32.984845005 + 33 t = -32.984845005 + 33 Combine like terms: -32.984845005 + 33 = 0.015154995 t = 0.015154995 Simplifying t = 0.015154995Solution
The solution to the problem is based on the solutions from the subproblems. t = {65.984845005, 0.015154995}
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