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Simplifying t2 + -2t = 3.14 Reorder the terms: -2t + t2 = 3.14 Solving -2t + t2 = 3.14 Solving for variable 't'. Reorder the terms: -3.14 + -2t + t2 = 3.14 + -3.14 Combine like terms: 3.14 + -3.14 = 0.00 -3.14 + -2t + t2 = 0.00 Begin completing the square. Move the constant term to the right: Add '3.14' to each side of the equation. -3.14 + -2t + 3.14 + t2 = 0.00 + 3.14 Reorder the terms: -3.14 + 3.14 + -2t + t2 = 0.00 + 3.14 Combine like terms: -3.14 + 3.14 = 0.00 0.00 + -2t + t2 = 0.00 + 3.14 -2t + t2 = 0.00 + 3.14 Combine like terms: 0.00 + 3.14 = 3.14 -2t + t2 = 3.14 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 = 3.14 + 1 Reorder the terms: 1 + -2t + t2 = 3.14 + 1 Combine like terms: 3.14 + 1 = 4.14 1 + -2t + t2 = 4.14 Factor a perfect square on the left side: (t + -1)(t + -1) = 4.14 Calculate the square root of the right side: 2.034698995 Break this problem into two subproblems by setting (t + -1) equal to 2.034698995 and -2.034698995.Subproblem 1
t + -1 = 2.034698995 Simplifying t + -1 = 2.034698995 Reorder the terms: -1 + t = 2.034698995 Solving -1 + t = 2.034698995 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 = 2.034698995 + 1 Combine like terms: -1 + 1 = 0 0 + t = 2.034698995 + 1 t = 2.034698995 + 1 Combine like terms: 2.034698995 + 1 = 3.034698995 t = 3.034698995 Simplifying t = 3.034698995Subproblem 2
t + -1 = -2.034698995 Simplifying t + -1 = -2.034698995 Reorder the terms: -1 + t = -2.034698995 Solving -1 + t = -2.034698995 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 = -2.034698995 + 1 Combine like terms: -1 + 1 = 0 0 + t = -2.034698995 + 1 t = -2.034698995 + 1 Combine like terms: -2.034698995 + 1 = -1.034698995 t = -1.034698995 Simplifying t = -1.034698995Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.034698995, -1.034698995}
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