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Simplifying -4.9t2 + 40t + 30 = 0 Reorder the terms: 30 + 40t + -4.9t2 = 0 Solving 30 + 40t + -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'. -6.12244898 + -8.163265306t + t2 = 0 Move the constant term to the right: Add '6.12244898' to each side of the equation. -6.12244898 + -8.163265306t + 6.12244898 + t2 = 0 + 6.12244898 Reorder the terms: -6.12244898 + 6.12244898 + -8.163265306t + t2 = 0 + 6.12244898 Combine like terms: -6.12244898 + 6.12244898 = 0.00000000 0.00000000 + -8.163265306t + t2 = 0 + 6.12244898 -8.163265306t + t2 = 0 + 6.12244898 Combine like terms: 0 + 6.12244898 = 6.12244898 -8.163265306t + t2 = 6.12244898 The t term is -8.163265306t. Take half its coefficient (-4.081632653). Square it (16.65972511) and add it to both sides. Add '16.65972511' to each side of the equation. -8.163265306t + 16.65972511 + t2 = 6.12244898 + 16.65972511 Reorder the terms: 16.65972511 + -8.163265306t + t2 = 6.12244898 + 16.65972511 Combine like terms: 6.12244898 + 16.65972511 = 22.78217409 16.65972511 + -8.163265306t + t2 = 22.78217409 Factor a perfect square on the left side: (t + -4.081632653)(t + -4.081632653) = 22.78217409 Calculate the square root of the right side: 4.773067577 Break this problem into two subproblems by setting (t + -4.081632653) equal to 4.773067577 and -4.773067577.Subproblem 1
t + -4.081632653 = 4.773067577 Simplifying t + -4.081632653 = 4.773067577 Reorder the terms: -4.081632653 + t = 4.773067577 Solving -4.081632653 + t = 4.773067577 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.081632653' to each side of the equation. -4.081632653 + 4.081632653 + t = 4.773067577 + 4.081632653 Combine like terms: -4.081632653 + 4.081632653 = 0.000000000 0.000000000 + t = 4.773067577 + 4.081632653 t = 4.773067577 + 4.081632653 Combine like terms: 4.773067577 + 4.081632653 = 8.85470023 t = 8.85470023 Simplifying t = 8.85470023Subproblem 2
t + -4.081632653 = -4.773067577 Simplifying t + -4.081632653 = -4.773067577 Reorder the terms: -4.081632653 + t = -4.773067577 Solving -4.081632653 + t = -4.773067577 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.081632653' to each side of the equation. -4.081632653 + 4.081632653 + t = -4.773067577 + 4.081632653 Combine like terms: -4.081632653 + 4.081632653 = 0.000000000 0.000000000 + t = -4.773067577 + 4.081632653 t = -4.773067577 + 4.081632653 Combine like terms: -4.773067577 + 4.081632653 = -0.691434924 t = -0.691434924 Simplifying t = -0.691434924Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.85470023, -0.691434924}
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