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Simplifying t2 + 2t = 1.2 Reorder the terms: 2t + t2 = 1.2 Solving 2t + t2 = 1.2 Solving for variable 't'. Reorder the terms: -1.2 + 2t + t2 = 1.2 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 -1.2 + 2t + t2 = 0.0 Begin completing the square. Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + 2t + 1.2 + t2 = 0.0 + 1.2 Reorder the terms: -1.2 + 1.2 + 2t + t2 = 0.0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + 2t + t2 = 0.0 + 1.2 2t + t2 = 0.0 + 1.2 Combine like terms: 0.0 + 1.2 = 1.2 2t + t2 = 1.2 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 = 1.2 + 1 Reorder the terms: 1 + 2t + t2 = 1.2 + 1 Combine like terms: 1.2 + 1 = 2.2 1 + 2t + t2 = 2.2 Factor a perfect square on the left side: (t + 1)(t + 1) = 2.2 Calculate the square root of the right side: 1.483239697 Break this problem into two subproblems by setting (t + 1) equal to 1.483239697 and -1.483239697.Subproblem 1
t + 1 = 1.483239697 Simplifying t + 1 = 1.483239697 Reorder the terms: 1 + t = 1.483239697 Solving 1 + t = 1.483239697 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 = 1.483239697 + -1 Combine like terms: 1 + -1 = 0 0 + t = 1.483239697 + -1 t = 1.483239697 + -1 Combine like terms: 1.483239697 + -1 = 0.483239697 t = 0.483239697 Simplifying t = 0.483239697Subproblem 2
t + 1 = -1.483239697 Simplifying t + 1 = -1.483239697 Reorder the terms: 1 + t = -1.483239697 Solving 1 + t = -1.483239697 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 = -1.483239697 + -1 Combine like terms: 1 + -1 = 0 0 + t = -1.483239697 + -1 t = -1.483239697 + -1 Combine like terms: -1.483239697 + -1 = -2.483239697 t = -2.483239697 Simplifying t = -2.483239697Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.483239697, -2.483239697}
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