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Simplifying 9t2 + -25t + -25 = 0 Reorder the terms: -25 + -25t + 9t2 = 0 Solving -25 + -25t + 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'. -2.777777778 + -2.777777778t + t2 = 0 Move the constant term to the right: Add '2.777777778' to each side of the equation. -2.777777778 + -2.777777778t + 2.777777778 + t2 = 0 + 2.777777778 Reorder the terms: -2.777777778 + 2.777777778 + -2.777777778t + t2 = 0 + 2.777777778 Combine like terms: -2.777777778 + 2.777777778 = 0.000000000 0.000000000 + -2.777777778t + t2 = 0 + 2.777777778 -2.777777778t + t2 = 0 + 2.777777778 Combine like terms: 0 + 2.777777778 = 2.777777778 -2.777777778t + t2 = 2.777777778 The t term is -2.777777778t. Take half its coefficient (-1.388888889). Square it (1.929012346) and add it to both sides. Add '1.929012346' to each side of the equation. -2.777777778t + 1.929012346 + t2 = 2.777777778 + 1.929012346 Reorder the terms: 1.929012346 + -2.777777778t + t2 = 2.777777778 + 1.929012346 Combine like terms: 2.777777778 + 1.929012346 = 4.706790124 1.929012346 + -2.777777778t + t2 = 4.706790124 Factor a perfect square on the left side: (t + -1.388888889)(t + -1.388888889) = 4.706790124 Calculate the square root of the right side: 2.169513799 Break this problem into two subproblems by setting (t + -1.388888889) equal to 2.169513799 and -2.169513799.Subproblem 1
t + -1.388888889 = 2.169513799 Simplifying t + -1.388888889 = 2.169513799 Reorder the terms: -1.388888889 + t = 2.169513799 Solving -1.388888889 + t = 2.169513799 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.388888889' to each side of the equation. -1.388888889 + 1.388888889 + t = 2.169513799 + 1.388888889 Combine like terms: -1.388888889 + 1.388888889 = 0.000000000 0.000000000 + t = 2.169513799 + 1.388888889 t = 2.169513799 + 1.388888889 Combine like terms: 2.169513799 + 1.388888889 = 3.558402688 t = 3.558402688 Simplifying t = 3.558402688Subproblem 2
t + -1.388888889 = -2.169513799 Simplifying t + -1.388888889 = -2.169513799 Reorder the terms: -1.388888889 + t = -2.169513799 Solving -1.388888889 + t = -2.169513799 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.388888889' to each side of the equation. -1.388888889 + 1.388888889 + t = -2.169513799 + 1.388888889 Combine like terms: -1.388888889 + 1.388888889 = 0.000000000 0.000000000 + t = -2.169513799 + 1.388888889 t = -2.169513799 + 1.388888889 Combine like terms: -2.169513799 + 1.388888889 = -0.78062491 t = -0.78062491 Simplifying t = -0.78062491Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.558402688, -0.78062491}
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