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Simplifying 4.9t2 + 2.1t + -55 = 0 Reorder the terms: -55 + 2.1t + 4.9t2 = 0 Solving -55 + 2.1t + 4.9t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -11.2244898 + 0.4285714286t + t2 = 0 Move the constant term to the right: Add '11.2244898' to each side of the equation. -11.2244898 + 0.4285714286t + 11.2244898 + t2 = 0 + 11.2244898 Reorder the terms: -11.2244898 + 11.2244898 + 0.4285714286t + t2 = 0 + 11.2244898 Combine like terms: -11.2244898 + 11.2244898 = 0.0000000 0.0000000 + 0.4285714286t + t2 = 0 + 11.2244898 0.4285714286t + t2 = 0 + 11.2244898 Combine like terms: 0 + 11.2244898 = 11.2244898 0.4285714286t + t2 = 11.2244898 The t term is 0.4285714286t. Take half its coefficient (0.2142857143). Square it (0.04591836735) and add it to both sides. Add '0.04591836735' to each side of the equation. 0.4285714286t + 0.04591836735 + t2 = 11.2244898 + 0.04591836735 Reorder the terms: 0.04591836735 + 0.4285714286t + t2 = 11.2244898 + 0.04591836735 Combine like terms: 11.2244898 + 0.04591836735 = 11.27040816735 0.04591836735 + 0.4285714286t + t2 = 11.27040816735 Factor a perfect square on the left side: (t + 0.2142857143)(t + 0.2142857143) = 11.27040816735 Calculate the square root of the right side: 3.357142858 Break this problem into two subproblems by setting (t + 0.2142857143) equal to 3.357142858 and -3.357142858.Subproblem 1
t + 0.2142857143 = 3.357142858 Simplifying t + 0.2142857143 = 3.357142858 Reorder the terms: 0.2142857143 + t = 3.357142858 Solving 0.2142857143 + t = 3.357142858 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.2142857143' to each side of the equation. 0.2142857143 + -0.2142857143 + t = 3.357142858 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + t = 3.357142858 + -0.2142857143 t = 3.357142858 + -0.2142857143 Combine like terms: 3.357142858 + -0.2142857143 = 3.1428571437 t = 3.1428571437 Simplifying t = 3.1428571437Subproblem 2
t + 0.2142857143 = -3.357142858 Simplifying t + 0.2142857143 = -3.357142858 Reorder the terms: 0.2142857143 + t = -3.357142858 Solving 0.2142857143 + t = -3.357142858 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.2142857143' to each side of the equation. 0.2142857143 + -0.2142857143 + t = -3.357142858 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + t = -3.357142858 + -0.2142857143 t = -3.357142858 + -0.2142857143 Combine like terms: -3.357142858 + -0.2142857143 = -3.5714285723 t = -3.5714285723 Simplifying t = -3.5714285723Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.1428571437, -3.5714285723}
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