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Simplifying 200 = 5t + 4.9t2 Solving 200 = 5t + 4.9t2 Solving for variable 't'. Reorder the terms: 200 + -5t + -4.9t2 = 5t + -5t + 4.9t2 + -4.9t2 Combine like terms: 5t + -5t = 0 200 + -5t + -4.9t2 = 0 + 4.9t2 + -4.9t2 200 + -5t + -4.9t2 = 4.9t2 + -4.9t2 Combine like terms: 4.9t2 + -4.9t2 = 0.0 200 + -5t + -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'. -40.81632653 + 1.020408163t + t2 = 0 Move the constant term to the right: Add '40.81632653' to each side of the equation. -40.81632653 + 1.020408163t + 40.81632653 + t2 = 0 + 40.81632653 Reorder the terms: -40.81632653 + 40.81632653 + 1.020408163t + t2 = 0 + 40.81632653 Combine like terms: -40.81632653 + 40.81632653 = 0.00000000 0.00000000 + 1.020408163t + t2 = 0 + 40.81632653 1.020408163t + t2 = 0 + 40.81632653 Combine like terms: 0 + 40.81632653 = 40.81632653 1.020408163t + t2 = 40.81632653 The t term is 1.020408163t. Take half its coefficient (0.5102040815). Square it (0.2603082048) and add it to both sides. Add '0.2603082048' to each side of the equation. 1.020408163t + 0.2603082048 + t2 = 40.81632653 + 0.2603082048 Reorder the terms: 0.2603082048 + 1.020408163t + t2 = 40.81632653 + 0.2603082048 Combine like terms: 40.81632653 + 0.2603082048 = 41.0766347348 0.2603082048 + 1.020408163t + t2 = 41.0766347348 Factor a perfect square on the left side: (t + 0.5102040815)(t + 0.5102040815) = 41.0766347348 Calculate the square root of the right side: 6.409105611 Break this problem into two subproblems by setting (t + 0.5102040815) equal to 6.409105611 and -6.409105611.Subproblem 1
t + 0.5102040815 = 6.409105611 Simplifying t + 0.5102040815 = 6.409105611 Reorder the terms: 0.5102040815 + t = 6.409105611 Solving 0.5102040815 + t = 6.409105611 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5102040815' to each side of the equation. 0.5102040815 + -0.5102040815 + t = 6.409105611 + -0.5102040815 Combine like terms: 0.5102040815 + -0.5102040815 = 0.0000000000 0.0000000000 + t = 6.409105611 + -0.5102040815 t = 6.409105611 + -0.5102040815 Combine like terms: 6.409105611 + -0.5102040815 = 5.8989015295 t = 5.8989015295 Simplifying t = 5.8989015295Subproblem 2
t + 0.5102040815 = -6.409105611 Simplifying t + 0.5102040815 = -6.409105611 Reorder the terms: 0.5102040815 + t = -6.409105611 Solving 0.5102040815 + t = -6.409105611 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5102040815' to each side of the equation. 0.5102040815 + -0.5102040815 + t = -6.409105611 + -0.5102040815 Combine like terms: 0.5102040815 + -0.5102040815 = 0.0000000000 0.0000000000 + t = -6.409105611 + -0.5102040815 t = -6.409105611 + -0.5102040815 Combine like terms: -6.409105611 + -0.5102040815 = -6.9193096925 t = -6.9193096925 Simplifying t = -6.9193096925Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.8989015295, -6.9193096925}
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