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Simplifying t2 + 2t = 17 Reorder the terms: 2t + t2 = 17 Solving 2t + t2 = 17 Solving for variable 't'. Reorder the terms: -17 + 2t + t2 = 17 + -17 Combine like terms: 17 + -17 = 0 -17 + 2t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '17' to each side of the equation. -17 + 2t + 17 + t2 = 0 + 17 Reorder the terms: -17 + 17 + 2t + t2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + 2t + t2 = 0 + 17 2t + t2 = 0 + 17 Combine like terms: 0 + 17 = 17 2t + t2 = 17 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 = 17 + 1 Reorder the terms: 1 + 2t + t2 = 17 + 1 Combine like terms: 17 + 1 = 18 1 + 2t + t2 = 18 Factor a perfect square on the left side: (t + 1)(t + 1) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (t + 1) equal to 4.242640687 and -4.242640687.Subproblem 1
t + 1 = 4.242640687 Simplifying t + 1 = 4.242640687 Reorder the terms: 1 + t = 4.242640687 Solving 1 + t = 4.242640687 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 = 4.242640687 + -1 Combine like terms: 1 + -1 = 0 0 + t = 4.242640687 + -1 t = 4.242640687 + -1 Combine like terms: 4.242640687 + -1 = 3.242640687 t = 3.242640687 Simplifying t = 3.242640687Subproblem 2
t + 1 = -4.242640687 Simplifying t + 1 = -4.242640687 Reorder the terms: 1 + t = -4.242640687 Solving 1 + t = -4.242640687 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 = -4.242640687 + -1 Combine like terms: 1 + -1 = 0 0 + t = -4.242640687 + -1 t = -4.242640687 + -1 Combine like terms: -4.242640687 + -1 = -5.242640687 t = -5.242640687 Simplifying t = -5.242640687Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.242640687, -5.242640687}
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