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Simplifying 4.905t2 + -8t + -30 = 0 Reorder the terms: -30 + -8t + 4.905t2 = 0 Solving -30 + -8t + 4.905t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 4.905 the coefficient of the squared term: Divide each side by '4.905'. -6.116207951 + -1.630988787t + t2 = 0 Move the constant term to the right: Add '6.116207951' to each side of the equation. -6.116207951 + -1.630988787t + 6.116207951 + t2 = 0 + 6.116207951 Reorder the terms: -6.116207951 + 6.116207951 + -1.630988787t + t2 = 0 + 6.116207951 Combine like terms: -6.116207951 + 6.116207951 = 0.000000000 0.000000000 + -1.630988787t + t2 = 0 + 6.116207951 -1.630988787t + t2 = 0 + 6.116207951 Combine like terms: 0 + 6.116207951 = 6.116207951 -1.630988787t + t2 = 6.116207951 The t term is -1.630988787t. Take half its coefficient (-0.8154943935). Square it (0.6650311058) and add it to both sides. Add '0.6650311058' to each side of the equation. -1.630988787t + 0.6650311058 + t2 = 6.116207951 + 0.6650311058 Reorder the terms: 0.6650311058 + -1.630988787t + t2 = 6.116207951 + 0.6650311058 Combine like terms: 6.116207951 + 0.6650311058 = 6.7812390568 0.6650311058 + -1.630988787t + t2 = 6.7812390568 Factor a perfect square on the left side: (t + -0.8154943935)(t + -0.8154943935) = 6.7812390568 Calculate the square root of the right side: 2.604081231 Break this problem into two subproblems by setting (t + -0.8154943935) equal to 2.604081231 and -2.604081231.Subproblem 1
t + -0.8154943935 = 2.604081231 Simplifying t + -0.8154943935 = 2.604081231 Reorder the terms: -0.8154943935 + t = 2.604081231 Solving -0.8154943935 + t = 2.604081231 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.8154943935' to each side of the equation. -0.8154943935 + 0.8154943935 + t = 2.604081231 + 0.8154943935 Combine like terms: -0.8154943935 + 0.8154943935 = 0.0000000000 0.0000000000 + t = 2.604081231 + 0.8154943935 t = 2.604081231 + 0.8154943935 Combine like terms: 2.604081231 + 0.8154943935 = 3.4195756245 t = 3.4195756245 Simplifying t = 3.4195756245Subproblem 2
t + -0.8154943935 = -2.604081231 Simplifying t + -0.8154943935 = -2.604081231 Reorder the terms: -0.8154943935 + t = -2.604081231 Solving -0.8154943935 + t = -2.604081231 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.8154943935' to each side of the equation. -0.8154943935 + 0.8154943935 + t = -2.604081231 + 0.8154943935 Combine like terms: -0.8154943935 + 0.8154943935 = 0.0000000000 0.0000000000 + t = -2.604081231 + 0.8154943935 t = -2.604081231 + 0.8154943935 Combine like terms: -2.604081231 + 0.8154943935 = -1.7885868375 t = -1.7885868375 Simplifying t = -1.7885868375Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.4195756245, -1.7885868375}
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