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Simplifying 0 = 60.5 + 13.3t + -4.9t2 Solving 0 = 60.5 + 13.3t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -60.5 = -60.5 -60.5 + -13.3t + 4.9t2 = 60.5 + 13.3t + -4.9t2 + -60.5 + -13.3t + 4.9t2 Reorder the terms: -60.5 + -13.3t + 4.9t2 = 60.5 + -60.5 + 13.3t + -13.3t + -4.9t2 + 4.9t2 Combine like terms: 60.5 + -60.5 = 0.0 -60.5 + -13.3t + 4.9t2 = 0.0 + 13.3t + -13.3t + -4.9t2 + 4.9t2 -60.5 + -13.3t + 4.9t2 = 13.3t + -13.3t + -4.9t2 + 4.9t2 Combine like terms: 13.3t + -13.3t = 0.0 -60.5 + -13.3t + 4.9t2 = 0.0 + -4.9t2 + 4.9t2 -60.5 + -13.3t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -60.5 + -13.3t + 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'. -12.34693878 + -2.714285714t + t2 = 0 Move the constant term to the right: Add '12.34693878' to each side of the equation. -12.34693878 + -2.714285714t + 12.34693878 + t2 = 0 + 12.34693878 Reorder the terms: -12.34693878 + 12.34693878 + -2.714285714t + t2 = 0 + 12.34693878 Combine like terms: -12.34693878 + 12.34693878 = 0.00000000 0.00000000 + -2.714285714t + t2 = 0 + 12.34693878 -2.714285714t + t2 = 0 + 12.34693878 Combine like terms: 0 + 12.34693878 = 12.34693878 -2.714285714t + t2 = 12.34693878 The t term is -2.714285714t. Take half its coefficient (-1.357142857). Square it (1.841836734) and add it to both sides. Add '1.841836734' to each side of the equation. -2.714285714t + 1.841836734 + t2 = 12.34693878 + 1.841836734 Reorder the terms: 1.841836734 + -2.714285714t + t2 = 12.34693878 + 1.841836734 Combine like terms: 12.34693878 + 1.841836734 = 14.188775514 1.841836734 + -2.714285714t + t2 = 14.188775514 Factor a perfect square on the left side: (t + -1.357142857)(t + -1.357142857) = 14.188775514 Calculate the square root of the right side: 3.766799107 Break this problem into two subproblems by setting (t + -1.357142857) equal to 3.766799107 and -3.766799107.Subproblem 1
t + -1.357142857 = 3.766799107 Simplifying t + -1.357142857 = 3.766799107 Reorder the terms: -1.357142857 + t = 3.766799107 Solving -1.357142857 + t = 3.766799107 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.357142857' to each side of the equation. -1.357142857 + 1.357142857 + t = 3.766799107 + 1.357142857 Combine like terms: -1.357142857 + 1.357142857 = 0.000000000 0.000000000 + t = 3.766799107 + 1.357142857 t = 3.766799107 + 1.357142857 Combine like terms: 3.766799107 + 1.357142857 = 5.123941964 t = 5.123941964 Simplifying t = 5.123941964Subproblem 2
t + -1.357142857 = -3.766799107 Simplifying t + -1.357142857 = -3.766799107 Reorder the terms: -1.357142857 + t = -3.766799107 Solving -1.357142857 + t = -3.766799107 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.357142857' to each side of the equation. -1.357142857 + 1.357142857 + t = -3.766799107 + 1.357142857 Combine like terms: -1.357142857 + 1.357142857 = 0.000000000 0.000000000 + t = -3.766799107 + 1.357142857 t = -3.766799107 + 1.357142857 Combine like terms: -3.766799107 + 1.357142857 = -2.40965625 t = -2.40965625 Simplifying t = -2.40965625Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.123941964, -2.40965625}
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