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Simplifying 4.9t2 + -30t + 40 = 0 Reorder the terms: 40 + -30t + 4.9t2 = 0 Solving 40 + -30t + 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 + -6.12244898t + t2 = 0 Move the constant term to the right: Add '-8.163265306' to each side of the equation. 8.163265306 + -6.12244898t + -8.163265306 + t2 = 0 + -8.163265306 Reorder the terms: 8.163265306 + -8.163265306 + -6.12244898t + t2 = 0 + -8.163265306 Combine like terms: 8.163265306 + -8.163265306 = 0.000000000 0.000000000 + -6.12244898t + t2 = 0 + -8.163265306 -6.12244898t + t2 = 0 + -8.163265306 Combine like terms: 0 + -8.163265306 = -8.163265306 -6.12244898t + t2 = -8.163265306 The t term is -6.12244898t. Take half its coefficient (-3.06122449). Square it (9.371095378) and add it to both sides. Add '9.371095378' to each side of the equation. -6.12244898t + 9.371095378 + t2 = -8.163265306 + 9.371095378 Reorder the terms: 9.371095378 + -6.12244898t + t2 = -8.163265306 + 9.371095378 Combine like terms: -8.163265306 + 9.371095378 = 1.207830072 9.371095378 + -6.12244898t + t2 = 1.207830072 Factor a perfect square on the left side: (t + -3.06122449)(t + -3.06122449) = 1.207830072 Calculate the square root of the right side: 1.099013226 Break this problem into two subproblems by setting (t + -3.06122449) equal to 1.099013226 and -1.099013226.Subproblem 1
t + -3.06122449 = 1.099013226 Simplifying t + -3.06122449 = 1.099013226 Reorder the terms: -3.06122449 + t = 1.099013226 Solving -3.06122449 + t = 1.099013226 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.06122449' to each side of the equation. -3.06122449 + 3.06122449 + t = 1.099013226 + 3.06122449 Combine like terms: -3.06122449 + 3.06122449 = 0.00000000 0.00000000 + t = 1.099013226 + 3.06122449 t = 1.099013226 + 3.06122449 Combine like terms: 1.099013226 + 3.06122449 = 4.160237716 t = 4.160237716 Simplifying t = 4.160237716Subproblem 2
t + -3.06122449 = -1.099013226 Simplifying t + -3.06122449 = -1.099013226 Reorder the terms: -3.06122449 + t = -1.099013226 Solving -3.06122449 + t = -1.099013226 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.06122449' to each side of the equation. -3.06122449 + 3.06122449 + t = -1.099013226 + 3.06122449 Combine like terms: -3.06122449 + 3.06122449 = 0.00000000 0.00000000 + t = -1.099013226 + 3.06122449 t = -1.099013226 + 3.06122449 Combine like terms: -1.099013226 + 3.06122449 = 1.962211264 t = 1.962211264 Simplifying t = 1.962211264Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.160237716, 1.962211264}
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