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Simplifying 4.9t2 + 5.0t + -40 = 0 Reorder the terms: -40 + 5.0t + 4.9t2 = 0 Solving -40 + 5.0t + 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'. -8.163265306 + 1.020408163t + t2 = 0 Move the constant term to the right: Add '8.163265306' to each side of the equation. -8.163265306 + 1.020408163t + 8.163265306 + t2 = 0 + 8.163265306 Reorder the terms: -8.163265306 + 8.163265306 + 1.020408163t + t2 = 0 + 8.163265306 Combine like terms: -8.163265306 + 8.163265306 = 0.000000000 0.000000000 + 1.020408163t + t2 = 0 + 8.163265306 1.020408163t + t2 = 0 + 8.163265306 Combine like terms: 0 + 8.163265306 = 8.163265306 1.020408163t + t2 = 8.163265306 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 = 8.163265306 + 0.2603082048 Reorder the terms: 0.2603082048 + 1.020408163t + t2 = 8.163265306 + 0.2603082048 Combine like terms: 8.163265306 + 0.2603082048 = 8.4235735108 0.2603082048 + 1.020408163t + t2 = 8.4235735108 Factor a perfect square on the left side: (t + 0.5102040815)(t + 0.5102040815) = 8.4235735108 Calculate the square root of the right side: 2.902339317 Break this problem into two subproblems by setting (t + 0.5102040815) equal to 2.902339317 and -2.902339317.Subproblem 1
t + 0.5102040815 = 2.902339317 Simplifying t + 0.5102040815 = 2.902339317 Reorder the terms: 0.5102040815 + t = 2.902339317 Solving 0.5102040815 + t = 2.902339317 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 = 2.902339317 + -0.5102040815 Combine like terms: 0.5102040815 + -0.5102040815 = 0.0000000000 0.0000000000 + t = 2.902339317 + -0.5102040815 t = 2.902339317 + -0.5102040815 Combine like terms: 2.902339317 + -0.5102040815 = 2.3921352355 t = 2.3921352355 Simplifying t = 2.3921352355Subproblem 2
t + 0.5102040815 = -2.902339317 Simplifying t + 0.5102040815 = -2.902339317 Reorder the terms: 0.5102040815 + t = -2.902339317 Solving 0.5102040815 + t = -2.902339317 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 = -2.902339317 + -0.5102040815 Combine like terms: 0.5102040815 + -0.5102040815 = 0.0000000000 0.0000000000 + t = -2.902339317 + -0.5102040815 t = -2.902339317 + -0.5102040815 Combine like terms: -2.902339317 + -0.5102040815 = -3.4125433985 t = -3.4125433985 Simplifying t = -3.4125433985Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.3921352355, -3.4125433985}
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