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Simplifying 60 = -4.9t2 + 40t Reorder the terms: 60 = 40t + -4.9t2 Solving 60 = 40t + -4.9t2 Solving for variable 't'. Reorder the terms: 60 + -40t + 4.9t2 = 40t + -40t + -4.9t2 + 4.9t2 Combine like terms: 40t + -40t = 0 60 + -40t + 4.9t2 = 0 + -4.9t2 + 4.9t2 60 + -40t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 60 + -40t + 4.9t2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. 12.24489796 + -8.163265306t + t2 = 0 Move the constant term to the right: Add '-12.24489796' to each side of the equation. 12.24489796 + -8.163265306t + -12.24489796 + t2 = 0 + -12.24489796 Reorder the terms: 12.24489796 + -12.24489796 + -8.163265306t + t2 = 0 + -12.24489796 Combine like terms: 12.24489796 + -12.24489796 = 0.00000000 0.00000000 + -8.163265306t + t2 = 0 + -12.24489796 -8.163265306t + t2 = 0 + -12.24489796 Combine like terms: 0 + -12.24489796 = -12.24489796 -8.163265306t + t2 = -12.24489796 The t term is -8.163265306t. Take half its coefficient (-4.081632653). Square it (16.65972511) and add it to both sides. Add '16.65972511' to each side of the equation. -8.163265306t + 16.65972511 + t2 = -12.24489796 + 16.65972511 Reorder the terms: 16.65972511 + -8.163265306t + t2 = -12.24489796 + 16.65972511 Combine like terms: -12.24489796 + 16.65972511 = 4.41482715 16.65972511 + -8.163265306t + t2 = 4.41482715 Factor a perfect square on the left side: (t + -4.081632653)(t + -4.081632653) = 4.41482715 Calculate the square root of the right side: 2.101149007 Break this problem into two subproblems by setting (t + -4.081632653) equal to 2.101149007 and -2.101149007.Subproblem 1
t + -4.081632653 = 2.101149007 Simplifying t + -4.081632653 = 2.101149007 Reorder the terms: -4.081632653 + t = 2.101149007 Solving -4.081632653 + t = 2.101149007 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.081632653' to each side of the equation. -4.081632653 + 4.081632653 + t = 2.101149007 + 4.081632653 Combine like terms: -4.081632653 + 4.081632653 = 0.000000000 0.000000000 + t = 2.101149007 + 4.081632653 t = 2.101149007 + 4.081632653 Combine like terms: 2.101149007 + 4.081632653 = 6.18278166 t = 6.18278166 Simplifying t = 6.18278166Subproblem 2
t + -4.081632653 = -2.101149007 Simplifying t + -4.081632653 = -2.101149007 Reorder the terms: -4.081632653 + t = -2.101149007 Solving -4.081632653 + t = -2.101149007 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.081632653' to each side of the equation. -4.081632653 + 4.081632653 + t = -2.101149007 + 4.081632653 Combine like terms: -4.081632653 + 4.081632653 = 0.000000000 0.000000000 + t = -2.101149007 + 4.081632653 t = -2.101149007 + 4.081632653 Combine like terms: -2.101149007 + 4.081632653 = 1.980483646 t = 1.980483646 Simplifying t = 1.980483646Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.18278166, 1.980483646}
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