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Simplifying t2 + -12t + 35 = 1 Reorder the terms: 35 + -12t + t2 = 1 Solving 35 + -12t + t2 = 1 Solving for variable 't'. Reorder the terms: 35 + -1 + -12t + t2 = 1 + -1 Combine like terms: 35 + -1 = 34 34 + -12t + t2 = 1 + -1 Combine like terms: 1 + -1 = 0 34 + -12t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-34' to each side of the equation. 34 + -12t + -34 + t2 = 0 + -34 Reorder the terms: 34 + -34 + -12t + t2 = 0 + -34 Combine like terms: 34 + -34 = 0 0 + -12t + t2 = 0 + -34 -12t + t2 = 0 + -34 Combine like terms: 0 + -34 = -34 -12t + t2 = -34 The t term is -12t. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12t + 36 + t2 = -34 + 36 Reorder the terms: 36 + -12t + t2 = -34 + 36 Combine like terms: -34 + 36 = 2 36 + -12t + t2 = 2 Factor a perfect square on the left side: (t + -6)(t + -6) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (t + -6) equal to 1.414213562 and -1.414213562.Subproblem 1
t + -6 = 1.414213562 Simplifying t + -6 = 1.414213562 Reorder the terms: -6 + t = 1.414213562 Solving -6 + t = 1.414213562 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + t = 1.414213562 + 6 Combine like terms: -6 + 6 = 0 0 + t = 1.414213562 + 6 t = 1.414213562 + 6 Combine like terms: 1.414213562 + 6 = 7.414213562 t = 7.414213562 Simplifying t = 7.414213562Subproblem 2
t + -6 = -1.414213562 Simplifying t + -6 = -1.414213562 Reorder the terms: -6 + t = -1.414213562 Solving -6 + t = -1.414213562 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + t = -1.414213562 + 6 Combine like terms: -6 + 6 = 0 0 + t = -1.414213562 + 6 t = -1.414213562 + 6 Combine like terms: -1.414213562 + 6 = 4.585786438 t = 4.585786438 Simplifying t = 4.585786438Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.414213562, 4.585786438}
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