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Simplifying 2 = 4.9t2 + 3t Reorder the terms: 2 = 3t + 4.9t2 Solving 2 = 3t + 4.9t2 Solving for variable 't'. Reorder the terms: 2 + -3t + -4.9t2 = 3t + -3t + 4.9t2 + -4.9t2 Combine like terms: 3t + -3t = 0 2 + -3t + -4.9t2 = 0 + 4.9t2 + -4.9t2 2 + -3t + -4.9t2 = 4.9t2 + -4.9t2 Combine like terms: 4.9t2 + -4.9t2 = 0.0 2 + -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'. -0.4081632653 + 0.612244898t + t2 = 0 Move the constant term to the right: Add '0.4081632653' to each side of the equation. -0.4081632653 + 0.612244898t + 0.4081632653 + t2 = 0 + 0.4081632653 Reorder the terms: -0.4081632653 + 0.4081632653 + 0.612244898t + t2 = 0 + 0.4081632653 Combine like terms: -0.4081632653 + 0.4081632653 = 0.0000000000 0.0000000000 + 0.612244898t + t2 = 0 + 0.4081632653 0.612244898t + t2 = 0 + 0.4081632653 Combine like terms: 0 + 0.4081632653 = 0.4081632653 0.612244898t + t2 = 0.4081632653 The t term is 0.612244898t. Take half its coefficient (0.306122449). Square it (0.09371095378) and add it to both sides. Add '0.09371095378' to each side of the equation. 0.612244898t + 0.09371095378 + t2 = 0.4081632653 + 0.09371095378 Reorder the terms: 0.09371095378 + 0.612244898t + t2 = 0.4081632653 + 0.09371095378 Combine like terms: 0.4081632653 + 0.09371095378 = 0.50187421908 0.09371095378 + 0.612244898t + t2 = 0.50187421908 Factor a perfect square on the left side: (t + 0.306122449)(t + 0.306122449) = 0.50187421908 Calculate the square root of the right side: 0.708430815 Break this problem into two subproblems by setting (t + 0.306122449) equal to 0.708430815 and -0.708430815.Subproblem 1
t + 0.306122449 = 0.708430815 Simplifying t + 0.306122449 = 0.708430815 Reorder the terms: 0.306122449 + t = 0.708430815 Solving 0.306122449 + t = 0.708430815 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.306122449' to each side of the equation. 0.306122449 + -0.306122449 + t = 0.708430815 + -0.306122449 Combine like terms: 0.306122449 + -0.306122449 = 0.000000000 0.000000000 + t = 0.708430815 + -0.306122449 t = 0.708430815 + -0.306122449 Combine like terms: 0.708430815 + -0.306122449 = 0.402308366 t = 0.402308366 Simplifying t = 0.402308366Subproblem 2
t + 0.306122449 = -0.708430815 Simplifying t + 0.306122449 = -0.708430815 Reorder the terms: 0.306122449 + t = -0.708430815 Solving 0.306122449 + t = -0.708430815 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.306122449' to each side of the equation. 0.306122449 + -0.306122449 + t = -0.708430815 + -0.306122449 Combine like terms: 0.306122449 + -0.306122449 = 0.000000000 0.000000000 + t = -0.708430815 + -0.306122449 t = -0.708430815 + -0.306122449 Combine like terms: -0.708430815 + -0.306122449 = -1.014553264 t = -1.014553264 Simplifying t = -1.014553264Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.402308366, -1.014553264}
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