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Simplifying 0 = 4.9t2 + 39.5t + 3 Reorder the terms: 0 = 3 + 39.5t + 4.9t2 Solving 0 = 3 + 39.5t + 4.9t2 Solving for variable 't'. Combine like terms: 0 + -3 = -3 -3 + -39.5t + -4.9t2 = 3 + 39.5t + 4.9t2 + -3 + -39.5t + -4.9t2 Reorder the terms: -3 + -39.5t + -4.9t2 = 3 + -3 + 39.5t + -39.5t + 4.9t2 + -4.9t2 Combine like terms: 3 + -3 = 0 -3 + -39.5t + -4.9t2 = 0 + 39.5t + -39.5t + 4.9t2 + -4.9t2 -3 + -39.5t + -4.9t2 = 39.5t + -39.5t + 4.9t2 + -4.9t2 Combine like terms: 39.5t + -39.5t = 0.0 -3 + -39.5t + -4.9t2 = 0.0 + 4.9t2 + -4.9t2 -3 + -39.5t + -4.9t2 = 4.9t2 + -4.9t2 Combine like terms: 4.9t2 + -4.9t2 = 0.0 -3 + -39.5t + -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'. 0.612244898 + 8.06122449t + t2 = 0 Move the constant term to the right: Add '-0.612244898' to each side of the equation. 0.612244898 + 8.06122449t + -0.612244898 + t2 = 0 + -0.612244898 Reorder the terms: 0.612244898 + -0.612244898 + 8.06122449t + t2 = 0 + -0.612244898 Combine like terms: 0.612244898 + -0.612244898 = 0.000000000 0.000000000 + 8.06122449t + t2 = 0 + -0.612244898 8.06122449t + t2 = 0 + -0.612244898 Combine like terms: 0 + -0.612244898 = -0.612244898 8.06122449t + t2 = -0.612244898 The t term is 8.06122449t. Take half its coefficient (4.030612245). Square it (16.24583507) and add it to both sides. Add '16.24583507' to each side of the equation. 8.06122449t + 16.24583507 + t2 = -0.612244898 + 16.24583507 Reorder the terms: 16.24583507 + 8.06122449t + t2 = -0.612244898 + 16.24583507 Combine like terms: -0.612244898 + 16.24583507 = 15.633590172 16.24583507 + 8.06122449t + t2 = 15.633590172 Factor a perfect square on the left side: (t + 4.030612245)(t + 4.030612245) = 15.633590172 Calculate the square root of the right side: 3.953933506 Break this problem into two subproblems by setting (t + 4.030612245) equal to 3.953933506 and -3.953933506.Subproblem 1
t + 4.030612245 = 3.953933506 Simplifying t + 4.030612245 = 3.953933506 Reorder the terms: 4.030612245 + t = 3.953933506 Solving 4.030612245 + t = 3.953933506 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-4.030612245' to each side of the equation. 4.030612245 + -4.030612245 + t = 3.953933506 + -4.030612245 Combine like terms: 4.030612245 + -4.030612245 = 0.000000000 0.000000000 + t = 3.953933506 + -4.030612245 t = 3.953933506 + -4.030612245 Combine like terms: 3.953933506 + -4.030612245 = -0.076678739 t = -0.076678739 Simplifying t = -0.076678739Subproblem 2
t + 4.030612245 = -3.953933506 Simplifying t + 4.030612245 = -3.953933506 Reorder the terms: 4.030612245 + t = -3.953933506 Solving 4.030612245 + t = -3.953933506 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-4.030612245' to each side of the equation. 4.030612245 + -4.030612245 + t = -3.953933506 + -4.030612245 Combine like terms: 4.030612245 + -4.030612245 = 0.000000000 0.000000000 + t = -3.953933506 + -4.030612245 t = -3.953933506 + -4.030612245 Combine like terms: -3.953933506 + -4.030612245 = -7.984545751 t = -7.984545751 Simplifying t = -7.984545751Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.076678739, -7.984545751}
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