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Simplifying 9t2 + -54t + -17 = 0 Reorder the terms: -17 + -54t + 9t2 = 0 Solving -17 + -54t + 9t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.888888889 + -6t + t2 = 0 Move the constant term to the right: Add '1.888888889' to each side of the equation. -1.888888889 + -6t + 1.888888889 + t2 = 0 + 1.888888889 Reorder the terms: -1.888888889 + 1.888888889 + -6t + t2 = 0 + 1.888888889 Combine like terms: -1.888888889 + 1.888888889 = 0.000000000 0.000000000 + -6t + t2 = 0 + 1.888888889 -6t + t2 = 0 + 1.888888889 Combine like terms: 0 + 1.888888889 = 1.888888889 -6t + t2 = 1.888888889 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 = 1.888888889 + 9 Reorder the terms: 9 + -6t + t2 = 1.888888889 + 9 Combine like terms: 1.888888889 + 9 = 10.888888889 9 + -6t + t2 = 10.888888889 Factor a perfect square on the left side: (t + -3)(t + -3) = 10.888888889 Calculate the square root of the right side: 3.299831646 Break this problem into two subproblems by setting (t + -3) equal to 3.299831646 and -3.299831646.Subproblem 1
t + -3 = 3.299831646 Simplifying t + -3 = 3.299831646 Reorder the terms: -3 + t = 3.299831646 Solving -3 + t = 3.299831646 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 = 3.299831646 + 3 Combine like terms: -3 + 3 = 0 0 + t = 3.299831646 + 3 t = 3.299831646 + 3 Combine like terms: 3.299831646 + 3 = 6.299831646 t = 6.299831646 Simplifying t = 6.299831646Subproblem 2
t + -3 = -3.299831646 Simplifying t + -3 = -3.299831646 Reorder the terms: -3 + t = -3.299831646 Solving -3 + t = -3.299831646 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 = -3.299831646 + 3 Combine like terms: -3 + 3 = 0 0 + t = -3.299831646 + 3 t = -3.299831646 + 3 Combine like terms: -3.299831646 + 3 = -0.299831646 t = -0.299831646 Simplifying t = -0.299831646Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.299831646, -0.299831646}
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