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Simplifying t2 = 2 + 2t Solving t2 = 2 + 2t Solving for variable 't'. Reorder the terms: -2 + -2t + t2 = 2 + 2t + -2 + -2t Reorder the terms: -2 + -2t + t2 = 2 + -2 + 2t + -2t Combine like terms: 2 + -2 = 0 -2 + -2t + t2 = 0 + 2t + -2t -2 + -2t + t2 = 2t + -2t Combine like terms: 2t + -2t = 0 -2 + -2t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + -2t + 2 + t2 = 0 + 2 Reorder the terms: -2 + 2 + -2t + t2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -2t + t2 = 0 + 2 -2t + t2 = 0 + 2 Combine like terms: 0 + 2 = 2 -2t + t2 = 2 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 = 2 + 1 Reorder the terms: 1 + -2t + t2 = 2 + 1 Combine like terms: 2 + 1 = 3 1 + -2t + t2 = 3 Factor a perfect square on the left side: (t + -1)(t + -1) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (t + -1) equal to 1.732050808 and -1.732050808.Subproblem 1
t + -1 = 1.732050808 Simplifying t + -1 = 1.732050808 Reorder the terms: -1 + t = 1.732050808 Solving -1 + t = 1.732050808 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 = 1.732050808 + 1 Combine like terms: -1 + 1 = 0 0 + t = 1.732050808 + 1 t = 1.732050808 + 1 Combine like terms: 1.732050808 + 1 = 2.732050808 t = 2.732050808 Simplifying t = 2.732050808Subproblem 2
t + -1 = -1.732050808 Simplifying t + -1 = -1.732050808 Reorder the terms: -1 + t = -1.732050808 Solving -1 + t = -1.732050808 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 = -1.732050808 + 1 Combine like terms: -1 + 1 = 0 0 + t = -1.732050808 + 1 t = -1.732050808 + 1 Combine like terms: -1.732050808 + 1 = -0.732050808 t = -0.732050808 Simplifying t = -0.732050808Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.732050808, -0.732050808}
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