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Simplifying 200 = 4.9t2 + 7t Reorder the terms: 200 = 7t + 4.9t2 Solving 200 = 7t + 4.9t2 Solving for variable 't'. Reorder the terms: 200 + -7t + -4.9t2 = 7t + -7t + 4.9t2 + -4.9t2 Combine like terms: 7t + -7t = 0 200 + -7t + -4.9t2 = 0 + 4.9t2 + -4.9t2 200 + -7t + -4.9t2 = 4.9t2 + -4.9t2 Combine like terms: 4.9t2 + -4.9t2 = 0.0 200 + -7t + -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 + 1.428571429t + t2 = 0 Move the constant term to the right: Add '40.81632653' to each side of the equation. -40.81632653 + 1.428571429t + 40.81632653 + t2 = 0 + 40.81632653 Reorder the terms: -40.81632653 + 40.81632653 + 1.428571429t + t2 = 0 + 40.81632653 Combine like terms: -40.81632653 + 40.81632653 = 0.00000000 0.00000000 + 1.428571429t + t2 = 0 + 40.81632653 1.428571429t + t2 = 0 + 40.81632653 Combine like terms: 0 + 40.81632653 = 40.81632653 1.428571429t + t2 = 40.81632653 The t term is 1.428571429t. Take half its coefficient (0.7142857145). Square it (0.5102040819) and add it to both sides. Add '0.5102040819' to each side of the equation. 1.428571429t + 0.5102040819 + t2 = 40.81632653 + 0.5102040819 Reorder the terms: 0.5102040819 + 1.428571429t + t2 = 40.81632653 + 0.5102040819 Combine like terms: 40.81632653 + 0.5102040819 = 41.3265306119 0.5102040819 + 1.428571429t + t2 = 41.3265306119 Factor a perfect square on the left side: (t + 0.7142857145)(t + 0.7142857145) = 41.3265306119 Calculate the square root of the right side: 6.428571429 Break this problem into two subproblems by setting (t + 0.7142857145) equal to 6.428571429 and -6.428571429.Subproblem 1
t + 0.7142857145 = 6.428571429 Simplifying t + 0.7142857145 = 6.428571429 Reorder the terms: 0.7142857145 + t = 6.428571429 Solving 0.7142857145 + t = 6.428571429 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.7142857145' to each side of the equation. 0.7142857145 + -0.7142857145 + t = 6.428571429 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + t = 6.428571429 + -0.7142857145 t = 6.428571429 + -0.7142857145 Combine like terms: 6.428571429 + -0.7142857145 = 5.7142857145 t = 5.7142857145 Simplifying t = 5.7142857145Subproblem 2
t + 0.7142857145 = -6.428571429 Simplifying t + 0.7142857145 = -6.428571429 Reorder the terms: 0.7142857145 + t = -6.428571429 Solving 0.7142857145 + t = -6.428571429 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.7142857145' to each side of the equation. 0.7142857145 + -0.7142857145 + t = -6.428571429 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + t = -6.428571429 + -0.7142857145 t = -6.428571429 + -0.7142857145 Combine like terms: -6.428571429 + -0.7142857145 = -7.1428571435 t = -7.1428571435 Simplifying t = -7.1428571435Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.7142857145, -7.1428571435}
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