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Simplifying 4.9t2 + 10 + -18.72t = 0 Reorder the terms: 10 + -18.72t + 4.9t2 = 0 Solving 10 + -18.72t + 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'. 2.040816327 + -3.820408163t + t2 = 0 Move the constant term to the right: Add '-2.040816327' to each side of the equation. 2.040816327 + -3.820408163t + -2.040816327 + t2 = 0 + -2.040816327 Reorder the terms: 2.040816327 + -2.040816327 + -3.820408163t + t2 = 0 + -2.040816327 Combine like terms: 2.040816327 + -2.040816327 = 0.000000000 0.000000000 + -3.820408163t + t2 = 0 + -2.040816327 -3.820408163t + t2 = 0 + -2.040816327 Combine like terms: 0 + -2.040816327 = -2.040816327 -3.820408163t + t2 = -2.040816327 The t term is -3.820408163t. Take half its coefficient (-1.910204082). Square it (3.648879635) and add it to both sides. Add '3.648879635' to each side of the equation. -3.820408163t + 3.648879635 + t2 = -2.040816327 + 3.648879635 Reorder the terms: 3.648879635 + -3.820408163t + t2 = -2.040816327 + 3.648879635 Combine like terms: -2.040816327 + 3.648879635 = 1.608063308 3.648879635 + -3.820408163t + t2 = 1.608063308 Factor a perfect square on the left side: (t + -1.910204082)(t + -1.910204082) = 1.608063308 Calculate the square root of the right side: 1.268094361 Break this problem into two subproblems by setting (t + -1.910204082) equal to 1.268094361 and -1.268094361.Subproblem 1
t + -1.910204082 = 1.268094361 Simplifying t + -1.910204082 = 1.268094361 Reorder the terms: -1.910204082 + t = 1.268094361 Solving -1.910204082 + t = 1.268094361 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.910204082' to each side of the equation. -1.910204082 + 1.910204082 + t = 1.268094361 + 1.910204082 Combine like terms: -1.910204082 + 1.910204082 = 0.000000000 0.000000000 + t = 1.268094361 + 1.910204082 t = 1.268094361 + 1.910204082 Combine like terms: 1.268094361 + 1.910204082 = 3.178298443 t = 3.178298443 Simplifying t = 3.178298443Subproblem 2
t + -1.910204082 = -1.268094361 Simplifying t + -1.910204082 = -1.268094361 Reorder the terms: -1.910204082 + t = -1.268094361 Solving -1.910204082 + t = -1.268094361 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.910204082' to each side of the equation. -1.910204082 + 1.910204082 + t = -1.268094361 + 1.910204082 Combine like terms: -1.910204082 + 1.910204082 = 0.000000000 0.000000000 + t = -1.268094361 + 1.910204082 t = -1.268094361 + 1.910204082 Combine like terms: -1.268094361 + 1.910204082 = 0.642109721 t = 0.642109721 Simplifying t = 0.642109721Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.178298443, 0.642109721}
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