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Simplifying 1.4t2 + 6t + 1.4 = 0 Reorder the terms: 1.4 + 6t + 1.4t2 = 0 Solving 1.4 + 6t + 1.4t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 1.4 the coefficient of the squared term: Divide each side by '1.4'. 1 + 4.285714286t + t2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 4.285714286t + -1 + t2 = 0 + -1 Reorder the terms: 1 + -1 + 4.285714286t + t2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4.285714286t + t2 = 0 + -1 4.285714286t + t2 = 0 + -1 Combine like terms: 0 + -1 = -1 4.285714286t + t2 = -1 The t term is 4.285714286t. Take half its coefficient (2.142857143). Square it (4.591836735) and add it to both sides. Add '4.591836735' to each side of the equation. 4.285714286t + 4.591836735 + t2 = -1 + 4.591836735 Reorder the terms: 4.591836735 + 4.285714286t + t2 = -1 + 4.591836735 Combine like terms: -1 + 4.591836735 = 3.591836735 4.591836735 + 4.285714286t + t2 = 3.591836735 Factor a perfect square on the left side: (t + 2.142857143)(t + 2.142857143) = 3.591836735 Calculate the square root of the right side: 1.895214166 Break this problem into two subproblems by setting (t + 2.142857143) equal to 1.895214166 and -1.895214166.Subproblem 1
t + 2.142857143 = 1.895214166 Simplifying t + 2.142857143 = 1.895214166 Reorder the terms: 2.142857143 + t = 1.895214166 Solving 2.142857143 + t = 1.895214166 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.142857143' to each side of the equation. 2.142857143 + -2.142857143 + t = 1.895214166 + -2.142857143 Combine like terms: 2.142857143 + -2.142857143 = 0.000000000 0.000000000 + t = 1.895214166 + -2.142857143 t = 1.895214166 + -2.142857143 Combine like terms: 1.895214166 + -2.142857143 = -0.247642977 t = -0.247642977 Simplifying t = -0.247642977Subproblem 2
t + 2.142857143 = -1.895214166 Simplifying t + 2.142857143 = -1.895214166 Reorder the terms: 2.142857143 + t = -1.895214166 Solving 2.142857143 + t = -1.895214166 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.142857143' to each side of the equation. 2.142857143 + -2.142857143 + t = -1.895214166 + -2.142857143 Combine like terms: 2.142857143 + -2.142857143 = 0.000000000 0.000000000 + t = -1.895214166 + -2.142857143 t = -1.895214166 + -2.142857143 Combine like terms: -1.895214166 + -2.142857143 = -4.038071309 t = -4.038071309 Simplifying t = -4.038071309Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.247642977, -4.038071309}
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