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Simplifying t2 + 2t + -45 = 0 Reorder the terms: -45 + 2t + t2 = 0 Solving -45 + 2t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '45' to each side of the equation. -45 + 2t + 45 + t2 = 0 + 45 Reorder the terms: -45 + 45 + 2t + t2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + 2t + t2 = 0 + 45 2t + t2 = 0 + 45 Combine like terms: 0 + 45 = 45 2t + t2 = 45 The t term is 2t. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2t + 1 + t2 = 45 + 1 Reorder the terms: 1 + 2t + t2 = 45 + 1 Combine like terms: 45 + 1 = 46 1 + 2t + t2 = 46 Factor a perfect square on the left side: (t + 1)(t + 1) = 46 Calculate the square root of the right side: 6.782329983 Break this problem into two subproblems by setting (t + 1) equal to 6.782329983 and -6.782329983.Subproblem 1
t + 1 = 6.782329983 Simplifying t + 1 = 6.782329983 Reorder the terms: 1 + t = 6.782329983 Solving 1 + t = 6.782329983 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + t = 6.782329983 + -1 Combine like terms: 1 + -1 = 0 0 + t = 6.782329983 + -1 t = 6.782329983 + -1 Combine like terms: 6.782329983 + -1 = 5.782329983 t = 5.782329983 Simplifying t = 5.782329983Subproblem 2
t + 1 = -6.782329983 Simplifying t + 1 = -6.782329983 Reorder the terms: 1 + t = -6.782329983 Solving 1 + t = -6.782329983 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + t = -6.782329983 + -1 Combine like terms: 1 + -1 = 0 0 + t = -6.782329983 + -1 t = -6.782329983 + -1 Combine like terms: -6.782329983 + -1 = -7.782329983 t = -7.782329983 Simplifying t = -7.782329983Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.782329983, -7.782329983}
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