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Simplifying 0 = -16.53 + 4.9t2 + 13.79t Reorder the terms: 0 = -16.53 + 13.79t + 4.9t2 Solving 0 = -16.53 + 13.79t + 4.9t2 Solving for variable 't'. Combine like terms: 0 + 16.53 = 16.53 16.53 + -13.79t + -4.9t2 = -16.53 + 13.79t + 4.9t2 + 16.53 + -13.79t + -4.9t2 Reorder the terms: 16.53 + -13.79t + -4.9t2 = -16.53 + 16.53 + 13.79t + -13.79t + 4.9t2 + -4.9t2 Combine like terms: -16.53 + 16.53 = 0.00 16.53 + -13.79t + -4.9t2 = 0.00 + 13.79t + -13.79t + 4.9t2 + -4.9t2 16.53 + -13.79t + -4.9t2 = 13.79t + -13.79t + 4.9t2 + -4.9t2 Combine like terms: 13.79t + -13.79t = 0.00 16.53 + -13.79t + -4.9t2 = 0.00 + 4.9t2 + -4.9t2 16.53 + -13.79t + -4.9t2 = 4.9t2 + -4.9t2 Combine like terms: 4.9t2 + -4.9t2 = 0.0 16.53 + -13.79t + -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'. -3.373469388 + 2.814285714t + t2 = 0 Move the constant term to the right: Add '3.373469388' to each side of the equation. -3.373469388 + 2.814285714t + 3.373469388 + t2 = 0 + 3.373469388 Reorder the terms: -3.373469388 + 3.373469388 + 2.814285714t + t2 = 0 + 3.373469388 Combine like terms: -3.373469388 + 3.373469388 = 0.000000000 0.000000000 + 2.814285714t + t2 = 0 + 3.373469388 2.814285714t + t2 = 0 + 3.373469388 Combine like terms: 0 + 3.373469388 = 3.373469388 2.814285714t + t2 = 3.373469388 The t term is 2.814285714t. Take half its coefficient (1.407142857). Square it (1.980051020) and add it to both sides. Add '1.980051020' to each side of the equation. 2.814285714t + 1.980051020 + t2 = 3.373469388 + 1.980051020 Reorder the terms: 1.980051020 + 2.814285714t + t2 = 3.373469388 + 1.980051020 Combine like terms: 3.373469388 + 1.980051020 = 5.353520408 1.980051020 + 2.814285714t + t2 = 5.353520408 Factor a perfect square on the left side: (t + 1.407142857)(t + 1.407142857) = 5.353520408 Calculate the square root of the right side: 2.313767579 Break this problem into two subproblems by setting (t + 1.407142857) equal to 2.313767579 and -2.313767579.Subproblem 1
t + 1.407142857 = 2.313767579 Simplifying t + 1.407142857 = 2.313767579 Reorder the terms: 1.407142857 + t = 2.313767579 Solving 1.407142857 + t = 2.313767579 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.407142857' to each side of the equation. 1.407142857 + -1.407142857 + t = 2.313767579 + -1.407142857 Combine like terms: 1.407142857 + -1.407142857 = 0.000000000 0.000000000 + t = 2.313767579 + -1.407142857 t = 2.313767579 + -1.407142857 Combine like terms: 2.313767579 + -1.407142857 = 0.906624722 t = 0.906624722 Simplifying t = 0.906624722Subproblem 2
t + 1.407142857 = -2.313767579 Simplifying t + 1.407142857 = -2.313767579 Reorder the terms: 1.407142857 + t = -2.313767579 Solving 1.407142857 + t = -2.313767579 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.407142857' to each side of the equation. 1.407142857 + -1.407142857 + t = -2.313767579 + -1.407142857 Combine like terms: 1.407142857 + -1.407142857 = 0.000000000 0.000000000 + t = -2.313767579 + -1.407142857 t = -2.313767579 + -1.407142857 Combine like terms: -2.313767579 + -1.407142857 = -3.720910436 t = -3.720910436 Simplifying t = -3.720910436Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.906624722, -3.720910436}
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