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Simplifying 4.9t2 + 11t + -11.1 = 0 Reorder the terms: -11.1 + 11t + 4.9t2 = 0 Solving -11.1 + 11t + 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'. -2.265306122 + 2.244897959t + t2 = 0 Move the constant term to the right: Add '2.265306122' to each side of the equation. -2.265306122 + 2.244897959t + 2.265306122 + t2 = 0 + 2.265306122 Reorder the terms: -2.265306122 + 2.265306122 + 2.244897959t + t2 = 0 + 2.265306122 Combine like terms: -2.265306122 + 2.265306122 = 0.000000000 0.000000000 + 2.244897959t + t2 = 0 + 2.265306122 2.244897959t + t2 = 0 + 2.265306122 Combine like terms: 0 + 2.265306122 = 2.265306122 2.244897959t + t2 = 2.265306122 The t term is 2.244897959t. Take half its coefficient (1.12244898). Square it (1.259891713) and add it to both sides. Add '1.259891713' to each side of the equation. 2.244897959t + 1.259891713 + t2 = 2.265306122 + 1.259891713 Reorder the terms: 1.259891713 + 2.244897959t + t2 = 2.265306122 + 1.259891713 Combine like terms: 2.265306122 + 1.259891713 = 3.525197835 1.259891713 + 2.244897959t + t2 = 3.525197835 Factor a perfect square on the left side: (t + 1.12244898)(t + 1.12244898) = 3.525197835 Calculate the square root of the right side: 1.877551021 Break this problem into two subproblems by setting (t + 1.12244898) equal to 1.877551021 and -1.877551021.Subproblem 1
t + 1.12244898 = 1.877551021 Simplifying t + 1.12244898 = 1.877551021 Reorder the terms: 1.12244898 + t = 1.877551021 Solving 1.12244898 + t = 1.877551021 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.12244898' to each side of the equation. 1.12244898 + -1.12244898 + t = 1.877551021 + -1.12244898 Combine like terms: 1.12244898 + -1.12244898 = 0.00000000 0.00000000 + t = 1.877551021 + -1.12244898 t = 1.877551021 + -1.12244898 Combine like terms: 1.877551021 + -1.12244898 = 0.755102041 t = 0.755102041 Simplifying t = 0.755102041Subproblem 2
t + 1.12244898 = -1.877551021 Simplifying t + 1.12244898 = -1.877551021 Reorder the terms: 1.12244898 + t = -1.877551021 Solving 1.12244898 + t = -1.877551021 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.12244898' to each side of the equation. 1.12244898 + -1.12244898 + t = -1.877551021 + -1.12244898 Combine like terms: 1.12244898 + -1.12244898 = 0.00000000 0.00000000 + t = -1.877551021 + -1.12244898 t = -1.877551021 + -1.12244898 Combine like terms: -1.877551021 + -1.12244898 = -3.000000001 t = -3.000000001 Simplifying t = -3.000000001Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.755102041, -3.000000001}
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