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Simplifying t2 + -8t + -13 = 0 Reorder the terms: -13 + -8t + t2 = 0 Solving -13 + -8t + t2 = 0 Solving for variable 't'. Begin completing the square. 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 = 9.385164807 t = 9.385164807 Simplifying t = 9.385164807Subproblem 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 = -1.385164807 t = -1.385164807 Simplifying t = -1.385164807Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.385164807, -1.385164807}
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