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Simplifying 13t2 + -40t + 25 = 0 Reorder the terms: 25 + -40t + 13t2 = 0 Solving 25 + -40t + 13t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. 1.923076923 + -3.076923077t + t2 = 0 Move the constant term to the right: Add '-1.923076923' to each side of the equation. 1.923076923 + -3.076923077t + -1.923076923 + t2 = 0 + -1.923076923 Reorder the terms: 1.923076923 + -1.923076923 + -3.076923077t + t2 = 0 + -1.923076923 Combine like terms: 1.923076923 + -1.923076923 = 0.000000000 0.000000000 + -3.076923077t + t2 = 0 + -1.923076923 -3.076923077t + t2 = 0 + -1.923076923 Combine like terms: 0 + -1.923076923 = -1.923076923 -3.076923077t + t2 = -1.923076923 The t term is -3.076923077t. Take half its coefficient (-1.538461539). Square it (2.366863907) and add it to both sides. Add '2.366863907' to each side of the equation. -3.076923077t + 2.366863907 + t2 = -1.923076923 + 2.366863907 Reorder the terms: 2.366863907 + -3.076923077t + t2 = -1.923076923 + 2.366863907 Combine like terms: -1.923076923 + 2.366863907 = 0.443786984 2.366863907 + -3.076923077t + t2 = 0.443786984 Factor a perfect square on the left side: (t + -1.538461539)(t + -1.538461539) = 0.443786984 Calculate the square root of the right side: 0.666173389 Break this problem into two subproblems by setting (t + -1.538461539) equal to 0.666173389 and -0.666173389.Subproblem 1
t + -1.538461539 = 0.666173389 Simplifying t + -1.538461539 = 0.666173389 Reorder the terms: -1.538461539 + t = 0.666173389 Solving -1.538461539 + t = 0.666173389 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.538461539' to each side of the equation. -1.538461539 + 1.538461539 + t = 0.666173389 + 1.538461539 Combine like terms: -1.538461539 + 1.538461539 = 0.000000000 0.000000000 + t = 0.666173389 + 1.538461539 t = 0.666173389 + 1.538461539 Combine like terms: 0.666173389 + 1.538461539 = 2.204634928 t = 2.204634928 Simplifying t = 2.204634928Subproblem 2
t + -1.538461539 = -0.666173389 Simplifying t + -1.538461539 = -0.666173389 Reorder the terms: -1.538461539 + t = -0.666173389 Solving -1.538461539 + t = -0.666173389 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.538461539' to each side of the equation. -1.538461539 + 1.538461539 + t = -0.666173389 + 1.538461539 Combine like terms: -1.538461539 + 1.538461539 = 0.000000000 0.000000000 + t = -0.666173389 + 1.538461539 t = -0.666173389 + 1.538461539 Combine like terms: -0.666173389 + 1.538461539 = 0.87228815 t = 0.87228815 Simplifying t = 0.87228815Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.204634928, 0.87228815}
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