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Simplifying 0 = -4.9t2 + 30t + 12 Reorder the terms: 0 = 12 + 30t + -4.9t2 Solving 0 = 12 + 30t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -12 = -12 -12 + -30t + 4.9t2 = 12 + 30t + -4.9t2 + -12 + -30t + 4.9t2 Reorder the terms: -12 + -30t + 4.9t2 = 12 + -12 + 30t + -30t + -4.9t2 + 4.9t2 Combine like terms: 12 + -12 = 0 -12 + -30t + 4.9t2 = 0 + 30t + -30t + -4.9t2 + 4.9t2 -12 + -30t + 4.9t2 = 30t + -30t + -4.9t2 + 4.9t2 Combine like terms: 30t + -30t = 0 -12 + -30t + 4.9t2 = 0 + -4.9t2 + 4.9t2 -12 + -30t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -12 + -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'. -2.448979592 + -6.12244898t + t2 = 0 Move the constant term to the right: Add '2.448979592' to each side of the equation. -2.448979592 + -6.12244898t + 2.448979592 + t2 = 0 + 2.448979592 Reorder the terms: -2.448979592 + 2.448979592 + -6.12244898t + t2 = 0 + 2.448979592 Combine like terms: -2.448979592 + 2.448979592 = 0.000000000 0.000000000 + -6.12244898t + t2 = 0 + 2.448979592 -6.12244898t + t2 = 0 + 2.448979592 Combine like terms: 0 + 2.448979592 = 2.448979592 -6.12244898t + t2 = 2.448979592 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 = 2.448979592 + 9.371095378 Reorder the terms: 9.371095378 + -6.12244898t + t2 = 2.448979592 + 9.371095378 Combine like terms: 2.448979592 + 9.371095378 = 11.82007497 9.371095378 + -6.12244898t + t2 = 11.82007497 Factor a perfect square on the left side: (t + -3.06122449)(t + -3.06122449) = 11.82007497 Calculate the square root of the right side: 3.438033591 Break this problem into two subproblems by setting (t + -3.06122449) equal to 3.438033591 and -3.438033591.Subproblem 1
t + -3.06122449 = 3.438033591 Simplifying t + -3.06122449 = 3.438033591 Reorder the terms: -3.06122449 + t = 3.438033591 Solving -3.06122449 + t = 3.438033591 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 = 3.438033591 + 3.06122449 Combine like terms: -3.06122449 + 3.06122449 = 0.00000000 0.00000000 + t = 3.438033591 + 3.06122449 t = 3.438033591 + 3.06122449 Combine like terms: 3.438033591 + 3.06122449 = 6.499258081 t = 6.499258081 Simplifying t = 6.499258081Subproblem 2
t + -3.06122449 = -3.438033591 Simplifying t + -3.06122449 = -3.438033591 Reorder the terms: -3.06122449 + t = -3.438033591 Solving -3.06122449 + t = -3.438033591 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 = -3.438033591 + 3.06122449 Combine like terms: -3.06122449 + 3.06122449 = 0.00000000 0.00000000 + t = -3.438033591 + 3.06122449 t = -3.438033591 + 3.06122449 Combine like terms: -3.438033591 + 3.06122449 = -0.376809101 t = -0.376809101 Simplifying t = -0.376809101Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.499258081, -0.376809101}
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