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Simplifying -9t2 + -7t + 1 = 0 Reorder the terms: 1 + -7t + -9t2 = 0 Solving 1 + -7t + -9t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -0.1111111111 + 0.7777777778t + t2 = 0 Move the constant term to the right: Add '0.1111111111' to each side of the equation. -0.1111111111 + 0.7777777778t + 0.1111111111 + t2 = 0 + 0.1111111111 Reorder the terms: -0.1111111111 + 0.1111111111 + 0.7777777778t + t2 = 0 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + 0.7777777778t + t2 = 0 + 0.1111111111 0.7777777778t + t2 = 0 + 0.1111111111 Combine like terms: 0 + 0.1111111111 = 0.1111111111 0.7777777778t + t2 = 0.1111111111 The t term is 0.7777777778t. Take half its coefficient (0.3888888889). Square it (0.1512345679) and add it to both sides. Add '0.1512345679' to each side of the equation. 0.7777777778t + 0.1512345679 + t2 = 0.1111111111 + 0.1512345679 Reorder the terms: 0.1512345679 + 0.7777777778t + t2 = 0.1111111111 + 0.1512345679 Combine like terms: 0.1111111111 + 0.1512345679 = 0.262345679 0.1512345679 + 0.7777777778t + t2 = 0.262345679 Factor a perfect square on the left side: (t + 0.3888888889)(t + 0.3888888889) = 0.262345679 Calculate the square root of the right side: 0.512196914 Break this problem into two subproblems by setting (t + 0.3888888889) equal to 0.512196914 and -0.512196914.Subproblem 1
t + 0.3888888889 = 0.512196914 Simplifying t + 0.3888888889 = 0.512196914 Reorder the terms: 0.3888888889 + t = 0.512196914 Solving 0.3888888889 + t = 0.512196914 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.3888888889' to each side of the equation. 0.3888888889 + -0.3888888889 + t = 0.512196914 + -0.3888888889 Combine like terms: 0.3888888889 + -0.3888888889 = 0.0000000000 0.0000000000 + t = 0.512196914 + -0.3888888889 t = 0.512196914 + -0.3888888889 Combine like terms: 0.512196914 + -0.3888888889 = 0.1233080251 t = 0.1233080251 Simplifying t = 0.1233080251Subproblem 2
t + 0.3888888889 = -0.512196914 Simplifying t + 0.3888888889 = -0.512196914 Reorder the terms: 0.3888888889 + t = -0.512196914 Solving 0.3888888889 + t = -0.512196914 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.3888888889' to each side of the equation. 0.3888888889 + -0.3888888889 + t = -0.512196914 + -0.3888888889 Combine like terms: 0.3888888889 + -0.3888888889 = 0.0000000000 0.0000000000 + t = -0.512196914 + -0.3888888889 t = -0.512196914 + -0.3888888889 Combine like terms: -0.512196914 + -0.3888888889 = -0.9010858029 t = -0.9010858029 Simplifying t = -0.9010858029Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.1233080251, -0.9010858029}
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