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Simplifying 29t + 4.9t2 + -15 = 0 Reorder the terms: -15 + 29t + 4.9t2 = 0 Solving -15 + 29t + 4.9t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -3.06122449 + 5.918367347t + t2 = 0 Move the constant term to the right: Add '3.06122449' to each side of the equation. -3.06122449 + 5.918367347t + 3.06122449 + t2 = 0 + 3.06122449 Reorder the terms: -3.06122449 + 3.06122449 + 5.918367347t + t2 = 0 + 3.06122449 Combine like terms: -3.06122449 + 3.06122449 = 0.00000000 0.00000000 + 5.918367347t + t2 = 0 + 3.06122449 5.918367347t + t2 = 0 + 3.06122449 Combine like terms: 0 + 3.06122449 = 3.06122449 5.918367347t + t2 = 3.06122449 The t term is 5.918367347t. Take half its coefficient (2.959183674). Square it (8.756768016) and add it to both sides. Add '8.756768016' to each side of the equation. 5.918367347t + 8.756768016 + t2 = 3.06122449 + 8.756768016 Reorder the terms: 8.756768016 + 5.918367347t + t2 = 3.06122449 + 8.756768016 Combine like terms: 3.06122449 + 8.756768016 = 11.817992506 8.756768016 + 5.918367347t + t2 = 11.817992506 Factor a perfect square on the left side: (t + 2.959183674)(t + 2.959183674) = 11.817992506 Calculate the square root of the right side: 3.43773072 Break this problem into two subproblems by setting (t + 2.959183674) equal to 3.43773072 and -3.43773072.Subproblem 1
t + 2.959183674 = 3.43773072 Simplifying t + 2.959183674 = 3.43773072 Reorder the terms: 2.959183674 + t = 3.43773072 Solving 2.959183674 + t = 3.43773072 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.959183674' to each side of the equation. 2.959183674 + -2.959183674 + t = 3.43773072 + -2.959183674 Combine like terms: 2.959183674 + -2.959183674 = 0.000000000 0.000000000 + t = 3.43773072 + -2.959183674 t = 3.43773072 + -2.959183674 Combine like terms: 3.43773072 + -2.959183674 = 0.478547046 t = 0.478547046 Simplifying t = 0.478547046Subproblem 2
t + 2.959183674 = -3.43773072 Simplifying t + 2.959183674 = -3.43773072 Reorder the terms: 2.959183674 + t = -3.43773072 Solving 2.959183674 + t = -3.43773072 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.959183674' to each side of the equation. 2.959183674 + -2.959183674 + t = -3.43773072 + -2.959183674 Combine like terms: 2.959183674 + -2.959183674 = 0.000000000 0.000000000 + t = -3.43773072 + -2.959183674 t = -3.43773072 + -2.959183674 Combine like terms: -3.43773072 + -2.959183674 = -6.396914394 t = -6.396914394 Simplifying t = -6.396914394Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.478547046, -6.396914394}
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