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Simplifying 500 = 4.9t2 + 30t Reorder the terms: 500 = 30t + 4.9t2 Solving 500 = 30t + 4.9t2 Solving for variable 't'. Reorder the terms: 500 + -30t + -4.9t2 = 30t + -30t + 4.9t2 + -4.9t2 Combine like terms: 30t + -30t = 0 500 + -30t + -4.9t2 = 0 + 4.9t2 + -4.9t2 500 + -30t + -4.9t2 = 4.9t2 + -4.9t2 Combine like terms: 4.9t2 + -4.9t2 = 0.0 500 + -30t + -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'. -102.0408163 + 6.12244898t + t2 = 0 Move the constant term to the right: Add '102.0408163' to each side of the equation. -102.0408163 + 6.12244898t + 102.0408163 + t2 = 0 + 102.0408163 Reorder the terms: -102.0408163 + 102.0408163 + 6.12244898t + t2 = 0 + 102.0408163 Combine like terms: -102.0408163 + 102.0408163 = 0.0000000 0.0000000 + 6.12244898t + t2 = 0 + 102.0408163 6.12244898t + t2 = 0 + 102.0408163 Combine like terms: 0 + 102.0408163 = 102.0408163 6.12244898t + t2 = 102.0408163 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 = 102.0408163 + 9.371095378 Reorder the terms: 9.371095378 + 6.12244898t + t2 = 102.0408163 + 9.371095378 Combine like terms: 102.0408163 + 9.371095378 = 111.411911678 9.371095378 + 6.12244898t + t2 = 111.411911678 Factor a perfect square on the left side: (t + 3.06122449)(t + 3.06122449) = 111.411911678 Calculate the square root of the right side: 10.555184114 Break this problem into two subproblems by setting (t + 3.06122449) equal to 10.555184114 and -10.555184114.Subproblem 1
t + 3.06122449 = 10.555184114 Simplifying t + 3.06122449 = 10.555184114 Reorder the terms: 3.06122449 + t = 10.555184114 Solving 3.06122449 + t = 10.555184114 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 = 10.555184114 + -3.06122449 Combine like terms: 3.06122449 + -3.06122449 = 0.00000000 0.00000000 + t = 10.555184114 + -3.06122449 t = 10.555184114 + -3.06122449 Combine like terms: 10.555184114 + -3.06122449 = 7.493959624 t = 7.493959624 Simplifying t = 7.493959624Subproblem 2
t + 3.06122449 = -10.555184114 Simplifying t + 3.06122449 = -10.555184114 Reorder the terms: 3.06122449 + t = -10.555184114 Solving 3.06122449 + t = -10.555184114 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 = -10.555184114 + -3.06122449 Combine like terms: 3.06122449 + -3.06122449 = 0.00000000 0.00000000 + t = -10.555184114 + -3.06122449 t = -10.555184114 + -3.06122449 Combine like terms: -10.555184114 + -3.06122449 = -13.616408604 t = -13.616408604 Simplifying t = -13.616408604Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.493959624, -13.616408604}
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