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Simplifying 0 = 20 + 6t + -1t2 Solving 0 = 20 + 6t + -1t2 Solving for variable 't'. Combine like terms: 0 + -20 = -20 -20 + -6t + t2 = 20 + 6t + -1t2 + -20 + -6t + t2 Reorder the terms: -20 + -6t + t2 = 20 + -20 + 6t + -6t + -1t2 + t2 Combine like terms: 20 + -20 = 0 -20 + -6t + t2 = 0 + 6t + -6t + -1t2 + t2 -20 + -6t + t2 = 6t + -6t + -1t2 + t2 Combine like terms: 6t + -6t = 0 -20 + -6t + t2 = 0 + -1t2 + t2 -20 + -6t + t2 = -1t2 + t2 Combine like terms: -1t2 + t2 = 0 -20 + -6t + t2 = 0 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 = 8.385164807 t = 8.385164807 Simplifying t = 8.385164807Subproblem 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 = -2.385164807 t = -2.385164807 Simplifying t = -2.385164807Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.385164807, -2.385164807}
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