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Simplifying t2 + 6t + -20 = 0 Reorder the terms: -20 + 6t + t2 = 0 Solving -20 + 6t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + 6t + 20 + t2 = 0 + 20 Reorder the terms: -20 + 20 + 6t + t2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 6t + t2 = 0 + 20 6t + t2 = 0 + 20 Combine like terms: 0 + 20 = 20 6t + t2 = 20 The t term is 6t. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6t + 9 + t2 = 20 + 9 Reorder the terms: 9 + 6t + t2 = 20 + 9 Combine like terms: 20 + 9 = 29 9 + 6t + t2 = 29 Factor a perfect square on the left side: (t + 3)(t + 3) = 29 Calculate the square root of the right side: 5.385164807 Break this problem into two subproblems by setting (t + 3) equal to 5.385164807 and -5.385164807.Subproblem 1
t + 3 = 5.385164807 Simplifying t + 3 = 5.385164807 Reorder the terms: 3 + t = 5.385164807 Solving 3 + t = 5.385164807 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + t = 5.385164807 + -3 Combine like terms: 3 + -3 = 0 0 + t = 5.385164807 + -3 t = 5.385164807 + -3 Combine like terms: 5.385164807 + -3 = 2.385164807 t = 2.385164807 Simplifying t = 2.385164807Subproblem 2
t + 3 = -5.385164807 Simplifying t + 3 = -5.385164807 Reorder the terms: 3 + t = -5.385164807 Solving 3 + t = -5.385164807 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + t = -5.385164807 + -3 Combine like terms: 3 + -3 = 0 0 + t = -5.385164807 + -3 t = -5.385164807 + -3 Combine like terms: -5.385164807 + -3 = -8.385164807 t = -8.385164807 Simplifying t = -8.385164807Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.385164807, -8.385164807}
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