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Simplifying 3.9 = -0.00936t2 + 0.4391t + 2.76 Reorder the terms: 3.9 = 2.76 + 0.4391t + -0.00936t2 Solving 3.9 = 2.76 + 0.4391t + -0.00936t2 Solving for variable 't'. Combine like terms: 3.9 + -2.76 = 1.14 1.14 + -0.4391t + 0.00936t2 = 2.76 + 0.4391t + -0.00936t2 + -2.76 + -0.4391t + 0.00936t2 Reorder the terms: 1.14 + -0.4391t + 0.00936t2 = 2.76 + -2.76 + 0.4391t + -0.4391t + -0.00936t2 + 0.00936t2 Combine like terms: 2.76 + -2.76 = 0.00 1.14 + -0.4391t + 0.00936t2 = 0.00 + 0.4391t + -0.4391t + -0.00936t2 + 0.00936t2 1.14 + -0.4391t + 0.00936t2 = 0.4391t + -0.4391t + -0.00936t2 + 0.00936t2 Combine like terms: 0.4391t + -0.4391t = 0.0000 1.14 + -0.4391t + 0.00936t2 = 0.0000 + -0.00936t2 + 0.00936t2 1.14 + -0.4391t + 0.00936t2 = -0.00936t2 + 0.00936t2 Combine like terms: -0.00936t2 + 0.00936t2 = 0.00000 1.14 + -0.4391t + 0.00936t2 = 0.00000 Begin completing the square. Divide all terms by 0.00936 the coefficient of the squared term: Divide each side by '0.00936'. 121.7948718 + -46.91239316t + t2 = 0 Move the constant term to the right: Add '-121.7948718' to each side of the equation. 121.7948718 + -46.91239316t + -121.7948718 + t2 = 0 + -121.7948718 Reorder the terms: 121.7948718 + -121.7948718 + -46.91239316t + t2 = 0 + -121.7948718 Combine like terms: 121.7948718 + -121.7948718 = 0.0000000 0.0000000 + -46.91239316t + t2 = 0 + -121.7948718 -46.91239316t + t2 = 0 + -121.7948718 Combine like terms: 0 + -121.7948718 = -121.7948718 -46.91239316t + t2 = -121.7948718 The t term is -46.91239316t. Take half its coefficient (-23.45619658). Square it (550.1931580) and add it to both sides. Add '550.1931580' to each side of the equation. -46.91239316t + 550.1931580 + t2 = -121.7948718 + 550.1931580 Reorder the terms: 550.1931580 + -46.91239316t + t2 = -121.7948718 + 550.1931580 Combine like terms: -121.7948718 + 550.1931580 = 428.3982862 550.1931580 + -46.91239316t + t2 = 428.3982862 Factor a perfect square on the left side: (t + -23.45619658)(t + -23.45619658) = 428.3982862 Calculate the square root of the right side: 20.697784572 Break this problem into two subproblems by setting (t + -23.45619658) equal to 20.697784572 and -20.697784572.Subproblem 1
t + -23.45619658 = 20.697784572 Simplifying t + -23.45619658 = 20.697784572 Reorder the terms: -23.45619658 + t = 20.697784572 Solving -23.45619658 + t = 20.697784572 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '23.45619658' to each side of the equation. -23.45619658 + 23.45619658 + t = 20.697784572 + 23.45619658 Combine like terms: -23.45619658 + 23.45619658 = 0.00000000 0.00000000 + t = 20.697784572 + 23.45619658 t = 20.697784572 + 23.45619658 Combine like terms: 20.697784572 + 23.45619658 = 44.153981152 t = 44.153981152 Simplifying t = 44.153981152Subproblem 2
t + -23.45619658 = -20.697784572 Simplifying t + -23.45619658 = -20.697784572 Reorder the terms: -23.45619658 + t = -20.697784572 Solving -23.45619658 + t = -20.697784572 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '23.45619658' to each side of the equation. -23.45619658 + 23.45619658 + t = -20.697784572 + 23.45619658 Combine like terms: -23.45619658 + 23.45619658 = 0.00000000 0.00000000 + t = -20.697784572 + 23.45619658 t = -20.697784572 + 23.45619658 Combine like terms: -20.697784572 + 23.45619658 = 2.758412008 t = 2.758412008 Simplifying t = 2.758412008Solution
The solution to the problem is based on the solutions from the subproblems. t = {44.153981152, 2.758412008}
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