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Simplifying -4.9t2 + -4t + 200 = 0 Reorder the terms: 200 + -4t + -4.9t2 = 0 Solving 200 + -4t + -4.9t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -40.81632653 + 0.8163265306t + t2 = 0 Move the constant term to the right: Add '40.81632653' to each side of the equation. -40.81632653 + 0.8163265306t + 40.81632653 + t2 = 0 + 40.81632653 Reorder the terms: -40.81632653 + 40.81632653 + 0.8163265306t + t2 = 0 + 40.81632653 Combine like terms: -40.81632653 + 40.81632653 = 0.00000000 0.00000000 + 0.8163265306t + t2 = 0 + 40.81632653 0.8163265306t + t2 = 0 + 40.81632653 Combine like terms: 0 + 40.81632653 = 40.81632653 0.8163265306t + t2 = 40.81632653 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 = 40.81632653 + 0.1665972511 Reorder the terms: 0.1665972511 + 0.8163265306t + t2 = 40.81632653 + 0.1665972511 Combine like terms: 40.81632653 + 0.1665972511 = 40.9829237811 0.1665972511 + 0.8163265306t + t2 = 40.9829237811 Factor a perfect square on the left side: (t + 0.4081632653)(t + 0.4081632653) = 40.9829237811 Calculate the square root of the right side: 6.40179067 Break this problem into two subproblems by setting (t + 0.4081632653) equal to 6.40179067 and -6.40179067.Subproblem 1
t + 0.4081632653 = 6.40179067 Simplifying t + 0.4081632653 = 6.40179067 Reorder the terms: 0.4081632653 + t = 6.40179067 Solving 0.4081632653 + t = 6.40179067 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 = 6.40179067 + -0.4081632653 Combine like terms: 0.4081632653 + -0.4081632653 = 0.0000000000 0.0000000000 + t = 6.40179067 + -0.4081632653 t = 6.40179067 + -0.4081632653 Combine like terms: 6.40179067 + -0.4081632653 = 5.9936274047 t = 5.9936274047 Simplifying t = 5.9936274047Subproblem 2
t + 0.4081632653 = -6.40179067 Simplifying t + 0.4081632653 = -6.40179067 Reorder the terms: 0.4081632653 + t = -6.40179067 Solving 0.4081632653 + t = -6.40179067 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 = -6.40179067 + -0.4081632653 Combine like terms: 0.4081632653 + -0.4081632653 = 0.0000000000 0.0000000000 + t = -6.40179067 + -0.4081632653 t = -6.40179067 + -0.4081632653 Combine like terms: -6.40179067 + -0.4081632653 = -6.8099539353 t = -6.8099539353 Simplifying t = -6.8099539353Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.9936274047, -6.8099539353}
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