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Simplifying 0 = -16t2 + 115t + 7.19 Reorder the terms: 0 = 7.19 + 115t + -16t2 Solving 0 = 7.19 + 115t + -16t2 Solving for variable 't'. Combine like terms: 0 + -7.19 = -7.19 -7.19 + -115t + 16t2 = 7.19 + 115t + -16t2 + -7.19 + -115t + 16t2 Reorder the terms: -7.19 + -115t + 16t2 = 7.19 + -7.19 + 115t + -115t + -16t2 + 16t2 Combine like terms: 7.19 + -7.19 = 0.00 -7.19 + -115t + 16t2 = 0.00 + 115t + -115t + -16t2 + 16t2 -7.19 + -115t + 16t2 = 115t + -115t + -16t2 + 16t2 Combine like terms: 115t + -115t = 0 -7.19 + -115t + 16t2 = 0 + -16t2 + 16t2 -7.19 + -115t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -7.19 + -115t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.449375 + -7.1875t + t2 = 0 Move the constant term to the right: Add '0.449375' to each side of the equation. -0.449375 + -7.1875t + 0.449375 + t2 = 0 + 0.449375 Reorder the terms: -0.449375 + 0.449375 + -7.1875t + t2 = 0 + 0.449375 Combine like terms: -0.449375 + 0.449375 = 0.000000 0.000000 + -7.1875t + t2 = 0 + 0.449375 -7.1875t + t2 = 0 + 0.449375 Combine like terms: 0 + 0.449375 = 0.449375 -7.1875t + t2 = 0.449375 The t term is -7.1875t. Take half its coefficient (-3.59375). Square it (12.91503906) and add it to both sides. Add '12.91503906' to each side of the equation. -7.1875t + 12.91503906 + t2 = 0.449375 + 12.91503906 Reorder the terms: 12.91503906 + -7.1875t + t2 = 0.449375 + 12.91503906 Combine like terms: 0.449375 + 12.91503906 = 13.36441406 12.91503906 + -7.1875t + t2 = 13.36441406 Factor a perfect square on the left side: (t + -3.59375)(t + -3.59375) = 13.36441406 Calculate the square root of the right side: 3.655737143 Break this problem into two subproblems by setting (t + -3.59375) equal to 3.655737143 and -3.655737143.Subproblem 1
t + -3.59375 = 3.655737143 Simplifying t + -3.59375 = 3.655737143 Reorder the terms: -3.59375 + t = 3.655737143 Solving -3.59375 + t = 3.655737143 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.59375' to each side of the equation. -3.59375 + 3.59375 + t = 3.655737143 + 3.59375 Combine like terms: -3.59375 + 3.59375 = 0.00000 0.00000 + t = 3.655737143 + 3.59375 t = 3.655737143 + 3.59375 Combine like terms: 3.655737143 + 3.59375 = 7.249487143 t = 7.249487143 Simplifying t = 7.249487143Subproblem 2
t + -3.59375 = -3.655737143 Simplifying t + -3.59375 = -3.655737143 Reorder the terms: -3.59375 + t = -3.655737143 Solving -3.59375 + t = -3.655737143 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.59375' to each side of the equation. -3.59375 + 3.59375 + t = -3.655737143 + 3.59375 Combine like terms: -3.59375 + 3.59375 = 0.00000 0.00000 + t = -3.655737143 + 3.59375 t = -3.655737143 + 3.59375 Combine like terms: -3.655737143 + 3.59375 = -0.061987143 t = -0.061987143 Simplifying t = -0.061987143Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.249487143, -0.061987143}
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