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Simplifying 0 = -4.9t2 + 39.2t + 1.5 Reorder the terms: 0 = 1.5 + 39.2t + -4.9t2 Solving 0 = 1.5 + 39.2t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -1.5 = -1.5 -1.5 + -39.2t + 4.9t2 = 1.5 + 39.2t + -4.9t2 + -1.5 + -39.2t + 4.9t2 Reorder the terms: -1.5 + -39.2t + 4.9t2 = 1.5 + -1.5 + 39.2t + -39.2t + -4.9t2 + 4.9t2 Combine like terms: 1.5 + -1.5 = 0.0 -1.5 + -39.2t + 4.9t2 = 0.0 + 39.2t + -39.2t + -4.9t2 + 4.9t2 -1.5 + -39.2t + 4.9t2 = 39.2t + -39.2t + -4.9t2 + 4.9t2 Combine like terms: 39.2t + -39.2t = 0.0 -1.5 + -39.2t + 4.9t2 = 0.0 + -4.9t2 + 4.9t2 -1.5 + -39.2t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -1.5 + -39.2t + 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'. -0.306122449 + -8t + t2 = 0 Move the constant term to the right: Add '0.306122449' to each side of the equation. -0.306122449 + -8t + 0.306122449 + t2 = 0 + 0.306122449 Reorder the terms: -0.306122449 + 0.306122449 + -8t + t2 = 0 + 0.306122449 Combine like terms: -0.306122449 + 0.306122449 = 0.000000000 0.000000000 + -8t + t2 = 0 + 0.306122449 -8t + t2 = 0 + 0.306122449 Combine like terms: 0 + 0.306122449 = 0.306122449 -8t + t2 = 0.306122449 The t term is -8t. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8t + 16 + t2 = 0.306122449 + 16 Reorder the terms: 16 + -8t + t2 = 0.306122449 + 16 Combine like terms: 0.306122449 + 16 = 16.306122449 16 + -8t + t2 = 16.306122449 Factor a perfect square on the left side: (t + -4)(t + -4) = 16.306122449 Calculate the square root of the right side: 4.038084007 Break this problem into two subproblems by setting (t + -4) equal to 4.038084007 and -4.038084007.Subproblem 1
t + -4 = 4.038084007 Simplifying t + -4 = 4.038084007 Reorder the terms: -4 + t = 4.038084007 Solving -4 + t = 4.038084007 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = 4.038084007 + 4 Combine like terms: -4 + 4 = 0 0 + t = 4.038084007 + 4 t = 4.038084007 + 4 Combine like terms: 4.038084007 + 4 = 8.038084007 t = 8.038084007 Simplifying t = 8.038084007Subproblem 2
t + -4 = -4.038084007 Simplifying t + -4 = -4.038084007 Reorder the terms: -4 + t = -4.038084007 Solving -4 + t = -4.038084007 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = -4.038084007 + 4 Combine like terms: -4 + 4 = 0 0 + t = -4.038084007 + 4 t = -4.038084007 + 4 Combine like terms: -4.038084007 + 4 = -0.038084007 t = -0.038084007 Simplifying t = -0.038084007Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.038084007, -0.038084007}
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