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Simplifying 13 + -8t + -1t2 = 0 Solving 13 + -8t + -1t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -13 + 8t + t2 = 0 Move the constant term to the right: Add '13' to each side of the equation. -13 + 8t + 13 + t2 = 0 + 13 Reorder the terms: -13 + 13 + 8t + t2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 8t + t2 = 0 + 13 8t + t2 = 0 + 13 Combine like terms: 0 + 13 = 13 8t + t2 = 13 The t term is 8t. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8t + 16 + t2 = 13 + 16 Reorder the terms: 16 + 8t + t2 = 13 + 16 Combine like terms: 13 + 16 = 29 16 + 8t + t2 = 29 Factor a perfect square on the left side: (t + 4)(t + 4) = 29 Calculate the square root of the right side: 5.385164807 Break this problem into two subproblems by setting (t + 4) equal to 5.385164807 and -5.385164807.Subproblem 1
t + 4 = 5.385164807 Simplifying t + 4 = 5.385164807 Reorder the terms: 4 + t = 5.385164807 Solving 4 + t = 5.385164807 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + t = 5.385164807 + -4 Combine like terms: 4 + -4 = 0 0 + t = 5.385164807 + -4 t = 5.385164807 + -4 Combine like terms: 5.385164807 + -4 = 1.385164807 t = 1.385164807 Simplifying t = 1.385164807Subproblem 2
t + 4 = -5.385164807 Simplifying t + 4 = -5.385164807 Reorder the terms: 4 + t = -5.385164807 Solving 4 + t = -5.385164807 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + t = -5.385164807 + -4 Combine like terms: 4 + -4 = 0 0 + t = -5.385164807 + -4 t = -5.385164807 + -4 Combine like terms: -5.385164807 + -4 = -9.385164807 t = -9.385164807 Simplifying t = -9.385164807Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.385164807, -9.385164807}
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