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Simplifying 30 = 11t + -0.83t2 Solving 30 = 11t + -0.83t2 Solving for variable 't'. Reorder the terms: 30 + -11t + 0.83t2 = 11t + -11t + -0.83t2 + 0.83t2 Combine like terms: 11t + -11t = 0 30 + -11t + 0.83t2 = 0 + -0.83t2 + 0.83t2 30 + -11t + 0.83t2 = -0.83t2 + 0.83t2 Combine like terms: -0.83t2 + 0.83t2 = 0.00 30 + -11t + 0.83t2 = 0.00 Begin completing the square. Divide all terms by 0.83 the coefficient of the squared term: Divide each side by '0.83'. 36.14457831 + -13.25301205t + t2 = 0 Move the constant term to the right: Add '-36.14457831' to each side of the equation. 36.14457831 + -13.25301205t + -36.14457831 + t2 = 0 + -36.14457831 Reorder the terms: 36.14457831 + -36.14457831 + -13.25301205t + t2 = 0 + -36.14457831 Combine like terms: 36.14457831 + -36.14457831 = 0.00000000 0.00000000 + -13.25301205t + t2 = 0 + -36.14457831 -13.25301205t + t2 = 0 + -36.14457831 Combine like terms: 0 + -36.14457831 = -36.14457831 -13.25301205t + t2 = -36.14457831 The t term is -13.25301205t. Take half its coefficient (-6.626506025). Square it (43.91058210) and add it to both sides. Add '43.91058210' to each side of the equation. -13.25301205t + 43.91058210 + t2 = -36.14457831 + 43.91058210 Reorder the terms: 43.91058210 + -13.25301205t + t2 = -36.14457831 + 43.91058210 Combine like terms: -36.14457831 + 43.91058210 = 7.76600379 43.91058210 + -13.25301205t + t2 = 7.76600379 Factor a perfect square on the left side: (t + -6.626506025)(t + -6.626506025) = 7.76600379 Calculate the square root of the right side: 2.786755065 Break this problem into two subproblems by setting (t + -6.626506025) equal to 2.786755065 and -2.786755065.Subproblem 1
t + -6.626506025 = 2.786755065 Simplifying t + -6.626506025 = 2.786755065 Reorder the terms: -6.626506025 + t = 2.786755065 Solving -6.626506025 + t = 2.786755065 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.626506025' to each side of the equation. -6.626506025 + 6.626506025 + t = 2.786755065 + 6.626506025 Combine like terms: -6.626506025 + 6.626506025 = 0.000000000 0.000000000 + t = 2.786755065 + 6.626506025 t = 2.786755065 + 6.626506025 Combine like terms: 2.786755065 + 6.626506025 = 9.41326109 t = 9.41326109 Simplifying t = 9.41326109Subproblem 2
t + -6.626506025 = -2.786755065 Simplifying t + -6.626506025 = -2.786755065 Reorder the terms: -6.626506025 + t = -2.786755065 Solving -6.626506025 + t = -2.786755065 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.626506025' to each side of the equation. -6.626506025 + 6.626506025 + t = -2.786755065 + 6.626506025 Combine like terms: -6.626506025 + 6.626506025 = 0.000000000 0.000000000 + t = -2.786755065 + 6.626506025 t = -2.786755065 + 6.626506025 Combine like terms: -2.786755065 + 6.626506025 = 3.83975096 t = 3.83975096 Simplifying t = 3.83975096Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.41326109, 3.83975096}
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