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Simplifying 4.9t2 + -30t + -35 = 0 Reorder the terms: -35 + -30t + 4.9t2 = 0 Solving -35 + -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'. -7.142857143 + -6.12244898t + t2 = 0 Move the constant term to the right: Add '7.142857143' to each side of the equation. -7.142857143 + -6.12244898t + 7.142857143 + t2 = 0 + 7.142857143 Reorder the terms: -7.142857143 + 7.142857143 + -6.12244898t + t2 = 0 + 7.142857143 Combine like terms: -7.142857143 + 7.142857143 = 0.000000000 0.000000000 + -6.12244898t + t2 = 0 + 7.142857143 -6.12244898t + t2 = 0 + 7.142857143 Combine like terms: 0 + 7.142857143 = 7.142857143 -6.12244898t + t2 = 7.142857143 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 = 7.142857143 + 9.371095378 Reorder the terms: 9.371095378 + -6.12244898t + t2 = 7.142857143 + 9.371095378 Combine like terms: 7.142857143 + 9.371095378 = 16.513952521 9.371095378 + -6.12244898t + t2 = 16.513952521 Factor a perfect square on the left side: (t + -3.06122449)(t + -3.06122449) = 16.513952521 Calculate the square root of the right side: 4.063736276 Break this problem into two subproblems by setting (t + -3.06122449) equal to 4.063736276 and -4.063736276.Subproblem 1
t + -3.06122449 = 4.063736276 Simplifying t + -3.06122449 = 4.063736276 Reorder the terms: -3.06122449 + t = 4.063736276 Solving -3.06122449 + t = 4.063736276 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 = 4.063736276 + 3.06122449 Combine like terms: -3.06122449 + 3.06122449 = 0.00000000 0.00000000 + t = 4.063736276 + 3.06122449 t = 4.063736276 + 3.06122449 Combine like terms: 4.063736276 + 3.06122449 = 7.124960766 t = 7.124960766 Simplifying t = 7.124960766Subproblem 2
t + -3.06122449 = -4.063736276 Simplifying t + -3.06122449 = -4.063736276 Reorder the terms: -3.06122449 + t = -4.063736276 Solving -3.06122449 + t = -4.063736276 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 = -4.063736276 + 3.06122449 Combine like terms: -3.06122449 + 3.06122449 = 0.00000000 0.00000000 + t = -4.063736276 + 3.06122449 t = -4.063736276 + 3.06122449 Combine like terms: -4.063736276 + 3.06122449 = -1.002511786 t = -1.002511786 Simplifying t = -1.002511786Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.124960766, -1.002511786}
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