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Simplifying 4.9t2 + 7t + -500 = 0 Reorder the terms: -500 + 7t + 4.9t2 = 0 Solving -500 + 7t + 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'. -102.0408163 + 1.428571429t + t2 = 0 Move the constant term to the right: Add '102.0408163' to each side of the equation. -102.0408163 + 1.428571429t + 102.0408163 + t2 = 0 + 102.0408163 Reorder the terms: -102.0408163 + 102.0408163 + 1.428571429t + t2 = 0 + 102.0408163 Combine like terms: -102.0408163 + 102.0408163 = 0.0000000 0.0000000 + 1.428571429t + t2 = 0 + 102.0408163 1.428571429t + t2 = 0 + 102.0408163 Combine like terms: 0 + 102.0408163 = 102.0408163 1.428571429t + t2 = 102.0408163 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 = 102.0408163 + 0.5102040819 Reorder the terms: 0.5102040819 + 1.428571429t + t2 = 102.0408163 + 0.5102040819 Combine like terms: 102.0408163 + 0.5102040819 = 102.5510203819 0.5102040819 + 1.428571429t + t2 = 102.5510203819 Factor a perfect square on the left side: (t + 0.7142857145)(t + 0.7142857145) = 102.5510203819 Calculate the square root of the right side: 10.126747769 Break this problem into two subproblems by setting (t + 0.7142857145) equal to 10.126747769 and -10.126747769.Subproblem 1
t + 0.7142857145 = 10.126747769 Simplifying t + 0.7142857145 = 10.126747769 Reorder the terms: 0.7142857145 + t = 10.126747769 Solving 0.7142857145 + t = 10.126747769 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 = 10.126747769 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + t = 10.126747769 + -0.7142857145 t = 10.126747769 + -0.7142857145 Combine like terms: 10.126747769 + -0.7142857145 = 9.4124620545 t = 9.4124620545 Simplifying t = 9.4124620545Subproblem 2
t + 0.7142857145 = -10.126747769 Simplifying t + 0.7142857145 = -10.126747769 Reorder the terms: 0.7142857145 + t = -10.126747769 Solving 0.7142857145 + t = -10.126747769 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 = -10.126747769 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + t = -10.126747769 + -0.7142857145 t = -10.126747769 + -0.7142857145 Combine like terms: -10.126747769 + -0.7142857145 = -10.8410334835 t = -10.8410334835 Simplifying t = -10.8410334835Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.4124620545, -10.8410334835}
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