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Simplifying 0 = -4.8t2 + 19.6t + 58.8 Reorder the terms: 0 = 58.8 + 19.6t + -4.8t2 Solving 0 = 58.8 + 19.6t + -4.8t2 Solving for variable 't'. Combine like terms: 0 + -58.8 = -58.8 -58.8 + -19.6t + 4.8t2 = 58.8 + 19.6t + -4.8t2 + -58.8 + -19.6t + 4.8t2 Reorder the terms: -58.8 + -19.6t + 4.8t2 = 58.8 + -58.8 + 19.6t + -19.6t + -4.8t2 + 4.8t2 Combine like terms: 58.8 + -58.8 = 0.0 -58.8 + -19.6t + 4.8t2 = 0.0 + 19.6t + -19.6t + -4.8t2 + 4.8t2 -58.8 + -19.6t + 4.8t2 = 19.6t + -19.6t + -4.8t2 + 4.8t2 Combine like terms: 19.6t + -19.6t = 0.0 -58.8 + -19.6t + 4.8t2 = 0.0 + -4.8t2 + 4.8t2 -58.8 + -19.6t + 4.8t2 = -4.8t2 + 4.8t2 Combine like terms: -4.8t2 + 4.8t2 = 0.0 -58.8 + -19.6t + 4.8t2 = 0.0 Begin completing the square. Divide all terms by 4.8 the coefficient of the squared term: Divide each side by '4.8'. -12.25 + -4.083333333t + t2 = 0 Move the constant term to the right: Add '12.25' to each side of the equation. -12.25 + -4.083333333t + 12.25 + t2 = 0 + 12.25 Reorder the terms: -12.25 + 12.25 + -4.083333333t + t2 = 0 + 12.25 Combine like terms: -12.25 + 12.25 = 0.00 0.00 + -4.083333333t + t2 = 0 + 12.25 -4.083333333t + t2 = 0 + 12.25 Combine like terms: 0 + 12.25 = 12.25 -4.083333333t + t2 = 12.25 The t term is -4.083333333t. Take half its coefficient (-2.041666667). Square it (4.168402779) and add it to both sides. Add '4.168402779' to each side of the equation. -4.083333333t + 4.168402779 + t2 = 12.25 + 4.168402779 Reorder the terms: 4.168402779 + -4.083333333t + t2 = 12.25 + 4.168402779 Combine like terms: 12.25 + 4.168402779 = 16.418402779 4.168402779 + -4.083333333t + t2 = 16.418402779 Factor a perfect square on the left side: (t + -2.041666667)(t + -2.041666667) = 16.418402779 Calculate the square root of the right side: 4.05196283 Break this problem into two subproblems by setting (t + -2.041666667) equal to 4.05196283 and -4.05196283.Subproblem 1
t + -2.041666667 = 4.05196283 Simplifying t + -2.041666667 = 4.05196283 Reorder the terms: -2.041666667 + t = 4.05196283 Solving -2.041666667 + t = 4.05196283 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.041666667' to each side of the equation. -2.041666667 + 2.041666667 + t = 4.05196283 + 2.041666667 Combine like terms: -2.041666667 + 2.041666667 = 0.000000000 0.000000000 + t = 4.05196283 + 2.041666667 t = 4.05196283 + 2.041666667 Combine like terms: 4.05196283 + 2.041666667 = 6.093629497 t = 6.093629497 Simplifying t = 6.093629497Subproblem 2
t + -2.041666667 = -4.05196283 Simplifying t + -2.041666667 = -4.05196283 Reorder the terms: -2.041666667 + t = -4.05196283 Solving -2.041666667 + t = -4.05196283 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.041666667' to each side of the equation. -2.041666667 + 2.041666667 + t = -4.05196283 + 2.041666667 Combine like terms: -2.041666667 + 2.041666667 = 0.000000000 0.000000000 + t = -4.05196283 + 2.041666667 t = -4.05196283 + 2.041666667 Combine like terms: -4.05196283 + 2.041666667 = -2.010296163 t = -2.010296163 Simplifying t = -2.010296163Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.093629497, -2.010296163}
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