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Simplifying 0 = 40 + 5t + -4.9t2 Solving 0 = 40 + 5t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -40 = -40 -40 + -5t + 4.9t2 = 40 + 5t + -4.9t2 + -40 + -5t + 4.9t2 Reorder the terms: -40 + -5t + 4.9t2 = 40 + -40 + 5t + -5t + -4.9t2 + 4.9t2 Combine like terms: 40 + -40 = 0 -40 + -5t + 4.9t2 = 0 + 5t + -5t + -4.9t2 + 4.9t2 -40 + -5t + 4.9t2 = 5t + -5t + -4.9t2 + 4.9t2 Combine like terms: 5t + -5t = 0 -40 + -5t + 4.9t2 = 0 + -4.9t2 + 4.9t2 -40 + -5t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -40 + -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'. -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 = 3.4125433985 t = 3.4125433985 Simplifying t = 3.4125433985Subproblem 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 = -2.3921352355 t = -2.3921352355 Simplifying t = -2.3921352355Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.4125433985, -2.3921352355}
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