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Simplifying 1.057t2 + -8.259t + -1074.071 = 0 Reorder the terms: -1074.071 + -8.259t + 1.057t2 = 0 Solving -1074.071 + -8.259t + 1.057t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 1.057 the coefficient of the squared term: Divide each side by '1.057'. -1016.150426 + -7.813623463t + t2 = 0 Move the constant term to the right: Add '1016.150426' to each side of the equation. -1016.150426 + -7.813623463t + 1016.150426 + t2 = 0 + 1016.150426 Reorder the terms: -1016.150426 + 1016.150426 + -7.813623463t + t2 = 0 + 1016.150426 Combine like terms: -1016.150426 + 1016.150426 = 0.000000 0.000000 + -7.813623463t + t2 = 0 + 1016.150426 -7.813623463t + t2 = 0 + 1016.150426 Combine like terms: 0 + 1016.150426 = 1016.150426 -7.813623463t + t2 = 1016.150426 The t term is -7.813623463t. Take half its coefficient (-3.906811732). Square it (15.26317791) and add it to both sides. Add '15.26317791' to each side of the equation. -7.813623463t + 15.26317791 + t2 = 1016.150426 + 15.26317791 Reorder the terms: 15.26317791 + -7.813623463t + t2 = 1016.150426 + 15.26317791 Combine like terms: 1016.150426 + 15.26317791 = 1031.41360391 15.26317791 + -7.813623463t + t2 = 1031.41360391 Factor a perfect square on the left side: (t + -3.906811732)(t + -3.906811732) = 1031.41360391 Calculate the square root of the right side: 32.115628655 Break this problem into two subproblems by setting (t + -3.906811732) equal to 32.115628655 and -32.115628655.Subproblem 1
t + -3.906811732 = 32.115628655 Simplifying t + -3.906811732 = 32.115628655 Reorder the terms: -3.906811732 + t = 32.115628655 Solving -3.906811732 + t = 32.115628655 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.906811732' to each side of the equation. -3.906811732 + 3.906811732 + t = 32.115628655 + 3.906811732 Combine like terms: -3.906811732 + 3.906811732 = 0.000000000 0.000000000 + t = 32.115628655 + 3.906811732 t = 32.115628655 + 3.906811732 Combine like terms: 32.115628655 + 3.906811732 = 36.022440387 t = 36.022440387 Simplifying t = 36.022440387Subproblem 2
t + -3.906811732 = -32.115628655 Simplifying t + -3.906811732 = -32.115628655 Reorder the terms: -3.906811732 + t = -32.115628655 Solving -3.906811732 + t = -32.115628655 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.906811732' to each side of the equation. -3.906811732 + 3.906811732 + t = -32.115628655 + 3.906811732 Combine like terms: -3.906811732 + 3.906811732 = 0.000000000 0.000000000 + t = -32.115628655 + 3.906811732 t = -32.115628655 + 3.906811732 Combine like terms: -32.115628655 + 3.906811732 = -28.208816923 t = -28.208816923 Simplifying t = -28.208816923Solution
The solution to the problem is based on the solutions from the subproblems. t = {36.022440387, -28.208816923}
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