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Simplifying 1.4t2 + 6t + 2.8 = 0 Reorder the terms: 2.8 + 6t + 1.4t2 = 0 Solving 2.8 + 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'. 2 + 4.285714286t + t2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + 4.285714286t + -2 + t2 = 0 + -2 Reorder the terms: 2 + -2 + 4.285714286t + t2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 4.285714286t + t2 = 0 + -2 4.285714286t + t2 = 0 + -2 Combine like terms: 0 + -2 = -2 4.285714286t + t2 = -2 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 = -2 + 4.591836735 Reorder the terms: 4.591836735 + 4.285714286t + t2 = -2 + 4.591836735 Combine like terms: -2 + 4.591836735 = 2.591836735 4.591836735 + 4.285714286t + t2 = 2.591836735 Factor a perfect square on the left side: (t + 2.142857143)(t + 2.142857143) = 2.591836735 Calculate the square root of the right side: 1.609918239 Break this problem into two subproblems by setting (t + 2.142857143) equal to 1.609918239 and -1.609918239.Subproblem 1
t + 2.142857143 = 1.609918239 Simplifying t + 2.142857143 = 1.609918239 Reorder the terms: 2.142857143 + t = 1.609918239 Solving 2.142857143 + t = 1.609918239 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 = 1.609918239 + -2.142857143 Combine like terms: 2.142857143 + -2.142857143 = 0.000000000 0.000000000 + t = 1.609918239 + -2.142857143 t = 1.609918239 + -2.142857143 Combine like terms: 1.609918239 + -2.142857143 = -0.532938904 t = -0.532938904 Simplifying t = -0.532938904Subproblem 2
t + 2.142857143 = -1.609918239 Simplifying t + 2.142857143 = -1.609918239 Reorder the terms: 2.142857143 + t = -1.609918239 Solving 2.142857143 + t = -1.609918239 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 = -1.609918239 + -2.142857143 Combine like terms: 2.142857143 + -2.142857143 = 0.000000000 0.000000000 + t = -1.609918239 + -2.142857143 t = -1.609918239 + -2.142857143 Combine like terms: -1.609918239 + -2.142857143 = -3.752775382 t = -3.752775382 Simplifying t = -3.752775382Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.532938904, -3.752775382}
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