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Simplifying 0 = -4.9t2 + 30.5t + 8.5 Reorder the terms: 0 = 8.5 + 30.5t + -4.9t2 Solving 0 = 8.5 + 30.5t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -8.5 = -8.5 -8.5 + -30.5t + 4.9t2 = 8.5 + 30.5t + -4.9t2 + -8.5 + -30.5t + 4.9t2 Reorder the terms: -8.5 + -30.5t + 4.9t2 = 8.5 + -8.5 + 30.5t + -30.5t + -4.9t2 + 4.9t2 Combine like terms: 8.5 + -8.5 = 0.0 -8.5 + -30.5t + 4.9t2 = 0.0 + 30.5t + -30.5t + -4.9t2 + 4.9t2 -8.5 + -30.5t + 4.9t2 = 30.5t + -30.5t + -4.9t2 + 4.9t2 Combine like terms: 30.5t + -30.5t = 0.0 -8.5 + -30.5t + 4.9t2 = 0.0 + -4.9t2 + 4.9t2 -8.5 + -30.5t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -8.5 + -30.5t + 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'. -1.734693878 + -6.224489796t + t2 = 0 Move the constant term to the right: Add '1.734693878' to each side of the equation. -1.734693878 + -6.224489796t + 1.734693878 + t2 = 0 + 1.734693878 Reorder the terms: -1.734693878 + 1.734693878 + -6.224489796t + t2 = 0 + 1.734693878 Combine like terms: -1.734693878 + 1.734693878 = 0.000000000 0.000000000 + -6.224489796t + t2 = 0 + 1.734693878 -6.224489796t + t2 = 0 + 1.734693878 Combine like terms: 0 + 1.734693878 = 1.734693878 -6.224489796t + t2 = 1.734693878 The t term is -6.224489796t. Take half its coefficient (-3.112244898). Square it (9.686068305) and add it to both sides. Add '9.686068305' to each side of the equation. -6.224489796t + 9.686068305 + t2 = 1.734693878 + 9.686068305 Reorder the terms: 9.686068305 + -6.224489796t + t2 = 1.734693878 + 9.686068305 Combine like terms: 1.734693878 + 9.686068305 = 11.420762183 9.686068305 + -6.224489796t + t2 = 11.420762183 Factor a perfect square on the left side: (t + -3.112244898)(t + -3.112244898) = 11.420762183 Calculate the square root of the right side: 3.379461819 Break this problem into two subproblems by setting (t + -3.112244898) equal to 3.379461819 and -3.379461819.Subproblem 1
t + -3.112244898 = 3.379461819 Simplifying t + -3.112244898 = 3.379461819 Reorder the terms: -3.112244898 + t = 3.379461819 Solving -3.112244898 + t = 3.379461819 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.112244898' to each side of the equation. -3.112244898 + 3.112244898 + t = 3.379461819 + 3.112244898 Combine like terms: -3.112244898 + 3.112244898 = 0.000000000 0.000000000 + t = 3.379461819 + 3.112244898 t = 3.379461819 + 3.112244898 Combine like terms: 3.379461819 + 3.112244898 = 6.491706717 t = 6.491706717 Simplifying t = 6.491706717Subproblem 2
t + -3.112244898 = -3.379461819 Simplifying t + -3.112244898 = -3.379461819 Reorder the terms: -3.112244898 + t = -3.379461819 Solving -3.112244898 + t = -3.379461819 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.112244898' to each side of the equation. -3.112244898 + 3.112244898 + t = -3.379461819 + 3.112244898 Combine like terms: -3.112244898 + 3.112244898 = 0.000000000 0.000000000 + t = -3.379461819 + 3.112244898 t = -3.379461819 + 3.112244898 Combine like terms: -3.379461819 + 3.112244898 = -0.267216921 t = -0.267216921 Simplifying t = -0.267216921Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.491706717, -0.267216921}
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