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Simplifying t2 + -2t = 40 + -4t Reorder the terms: -2t + t2 = 40 + -4t Solving -2t + t2 = 40 + -4t Solving for variable 't'. Reorder the terms: -40 + -2t + 4t + t2 = 40 + -4t + -40 + 4t Combine like terms: -2t + 4t = 2t -40 + 2t + t2 = 40 + -4t + -40 + 4t Reorder the terms: -40 + 2t + t2 = 40 + -40 + -4t + 4t Combine like terms: 40 + -40 = 0 -40 + 2t + t2 = 0 + -4t + 4t -40 + 2t + t2 = -4t + 4t Combine like terms: -4t + 4t = 0 -40 + 2t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '40' to each side of the equation. -40 + 2t + 40 + t2 = 0 + 40 Reorder the terms: -40 + 40 + 2t + t2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + 2t + t2 = 0 + 40 2t + t2 = 0 + 40 Combine like terms: 0 + 40 = 40 2t + t2 = 40 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 = 40 + 1 Reorder the terms: 1 + 2t + t2 = 40 + 1 Combine like terms: 40 + 1 = 41 1 + 2t + t2 = 41 Factor a perfect square on the left side: (t + 1)(t + 1) = 41 Calculate the square root of the right side: 6.403124237 Break this problem into two subproblems by setting (t + 1) equal to 6.403124237 and -6.403124237.Subproblem 1
t + 1 = 6.403124237 Simplifying t + 1 = 6.403124237 Reorder the terms: 1 + t = 6.403124237 Solving 1 + t = 6.403124237 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 = 6.403124237 + -1 Combine like terms: 1 + -1 = 0 0 + t = 6.403124237 + -1 t = 6.403124237 + -1 Combine like terms: 6.403124237 + -1 = 5.403124237 t = 5.403124237 Simplifying t = 5.403124237Subproblem 2
t + 1 = -6.403124237 Simplifying t + 1 = -6.403124237 Reorder the terms: 1 + t = -6.403124237 Solving 1 + t = -6.403124237 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 = -6.403124237 + -1 Combine like terms: 1 + -1 = 0 0 + t = -6.403124237 + -1 t = -6.403124237 + -1 Combine like terms: -6.403124237 + -1 = -7.403124237 t = -7.403124237 Simplifying t = -7.403124237Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.403124237, -7.403124237}
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