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Simplifying 100000 = 5t + 0.5(9.8) * t2 Multiply 0.5 * 9.8 100000 = 5t + 4.9t2 Solving 100000 = 5t + 4.9t2 Solving for variable 't'. Reorder the terms: 100000 + -5t + -4.9t2 = 5t + -5t + 4.9t2 + -4.9t2 Combine like terms: 5t + -5t = 0 100000 + -5t + -4.9t2 = 0 + 4.9t2 + -4.9t2 100000 + -5t + -4.9t2 = 4.9t2 + -4.9t2 Combine like terms: 4.9t2 + -4.9t2 = 0.0 100000 + -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'. -20408.16327 + 1.020408163t + t2 = 0 Move the constant term to the right: Add '20408.16327' to each side of the equation. -20408.16327 + 1.020408163t + 20408.16327 + t2 = 0 + 20408.16327 Reorder the terms: -20408.16327 + 20408.16327 + 1.020408163t + t2 = 0 + 20408.16327 Combine like terms: -20408.16327 + 20408.16327 = 0.00000 0.00000 + 1.020408163t + t2 = 0 + 20408.16327 1.020408163t + t2 = 0 + 20408.16327 Combine like terms: 0 + 20408.16327 = 20408.16327 1.020408163t + t2 = 20408.16327 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 = 20408.16327 + 0.2603082048 Reorder the terms: 0.2603082048 + 1.020408163t + t2 = 20408.16327 + 0.2603082048 Combine like terms: 20408.16327 + 0.2603082048 = 20408.4235782048 0.2603082048 + 1.020408163t + t2 = 20408.4235782048 Factor a perfect square on the left side: (t + 0.5102040815)(t + 0.5102040815) = 20408.4235782048 Calculate the square root of the right side: 142.858053949 Break this problem into two subproblems by setting (t + 0.5102040815) equal to 142.858053949 and -142.858053949.Subproblem 1
t + 0.5102040815 = 142.858053949 Simplifying t + 0.5102040815 = 142.858053949 Reorder the terms: 0.5102040815 + t = 142.858053949 Solving 0.5102040815 + t = 142.858053949 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 = 142.858053949 + -0.5102040815 Combine like terms: 0.5102040815 + -0.5102040815 = 0.0000000000 0.0000000000 + t = 142.858053949 + -0.5102040815 t = 142.858053949 + -0.5102040815 Combine like terms: 142.858053949 + -0.5102040815 = 142.3478498675 t = 142.3478498675 Simplifying t = 142.3478498675Subproblem 2
t + 0.5102040815 = -142.858053949 Simplifying t + 0.5102040815 = -142.858053949 Reorder the terms: 0.5102040815 + t = -142.858053949 Solving 0.5102040815 + t = -142.858053949 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 = -142.858053949 + -0.5102040815 Combine like terms: 0.5102040815 + -0.5102040815 = 0.0000000000 0.0000000000 + t = -142.858053949 + -0.5102040815 t = -142.858053949 + -0.5102040815 Combine like terms: -142.858053949 + -0.5102040815 = -143.3682580305 t = -143.3682580305 Simplifying t = -143.3682580305Solution
The solution to the problem is based on the solutions from the subproblems. t = {142.3478498675, -143.3682580305}
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