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Simplifying 0 = -4.9t2 + -4t + 50 Reorder the terms: 0 = 50 + -4t + -4.9t2 Solving 0 = 50 + -4t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -50 = -50 -50 + 4t + 4.9t2 = 50 + -4t + -4.9t2 + -50 + 4t + 4.9t2 Reorder the terms: -50 + 4t + 4.9t2 = 50 + -50 + -4t + 4t + -4.9t2 + 4.9t2 Combine like terms: 50 + -50 = 0 -50 + 4t + 4.9t2 = 0 + -4t + 4t + -4.9t2 + 4.9t2 -50 + 4t + 4.9t2 = -4t + 4t + -4.9t2 + 4.9t2 Combine like terms: -4t + 4t = 0 -50 + 4t + 4.9t2 = 0 + -4.9t2 + 4.9t2 -50 + 4t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -50 + 4t + 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'. -10.20408163 + 0.8163265306t + t2 = 0 Move the constant term to the right: Add '10.20408163' to each side of the equation. -10.20408163 + 0.8163265306t + 10.20408163 + t2 = 0 + 10.20408163 Reorder the terms: -10.20408163 + 10.20408163 + 0.8163265306t + t2 = 0 + 10.20408163 Combine like terms: -10.20408163 + 10.20408163 = 0.00000000 0.00000000 + 0.8163265306t + t2 = 0 + 10.20408163 0.8163265306t + t2 = 0 + 10.20408163 Combine like terms: 0 + 10.20408163 = 10.20408163 0.8163265306t + t2 = 10.20408163 The t term is 0.8163265306t. Take half its coefficient (0.4081632653). Square it (0.1665972511) and add it to both sides. Add '0.1665972511' to each side of the equation. 0.8163265306t + 0.1665972511 + t2 = 10.20408163 + 0.1665972511 Reorder the terms: 0.1665972511 + 0.8163265306t + t2 = 10.20408163 + 0.1665972511 Combine like terms: 10.20408163 + 0.1665972511 = 10.3706788811 0.1665972511 + 0.8163265306t + t2 = 10.3706788811 Factor a perfect square on the left side: (t + 0.4081632653)(t + 0.4081632653) = 10.3706788811 Calculate the square root of the right side: 3.220353844 Break this problem into two subproblems by setting (t + 0.4081632653) equal to 3.220353844 and -3.220353844.Subproblem 1
t + 0.4081632653 = 3.220353844 Simplifying t + 0.4081632653 = 3.220353844 Reorder the terms: 0.4081632653 + t = 3.220353844 Solving 0.4081632653 + t = 3.220353844 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.4081632653' to each side of the equation. 0.4081632653 + -0.4081632653 + t = 3.220353844 + -0.4081632653 Combine like terms: 0.4081632653 + -0.4081632653 = 0.0000000000 0.0000000000 + t = 3.220353844 + -0.4081632653 t = 3.220353844 + -0.4081632653 Combine like terms: 3.220353844 + -0.4081632653 = 2.8121905787 t = 2.8121905787 Simplifying t = 2.8121905787Subproblem 2
t + 0.4081632653 = -3.220353844 Simplifying t + 0.4081632653 = -3.220353844 Reorder the terms: 0.4081632653 + t = -3.220353844 Solving 0.4081632653 + t = -3.220353844 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.4081632653' to each side of the equation. 0.4081632653 + -0.4081632653 + t = -3.220353844 + -0.4081632653 Combine like terms: 0.4081632653 + -0.4081632653 = 0.0000000000 0.0000000000 + t = -3.220353844 + -0.4081632653 t = -3.220353844 + -0.4081632653 Combine like terms: -3.220353844 + -0.4081632653 = -3.6285171093 t = -3.6285171093 Simplifying t = -3.6285171093Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.8121905787, -3.6285171093}
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