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Simplifying 0 = -4.9t2 + 11t + 600 Reorder the terms: 0 = 600 + 11t + -4.9t2 Solving 0 = 600 + 11t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -600 = -600 -600 + -11t + 4.9t2 = 600 + 11t + -4.9t2 + -600 + -11t + 4.9t2 Reorder the terms: -600 + -11t + 4.9t2 = 600 + -600 + 11t + -11t + -4.9t2 + 4.9t2 Combine like terms: 600 + -600 = 0 -600 + -11t + 4.9t2 = 0 + 11t + -11t + -4.9t2 + 4.9t2 -600 + -11t + 4.9t2 = 11t + -11t + -4.9t2 + 4.9t2 Combine like terms: 11t + -11t = 0 -600 + -11t + 4.9t2 = 0 + -4.9t2 + 4.9t2 -600 + -11t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -600 + -11t + 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'. -122.4489796 + -2.244897959t + t2 = 0 Move the constant term to the right: Add '122.4489796' to each side of the equation. -122.4489796 + -2.244897959t + 122.4489796 + t2 = 0 + 122.4489796 Reorder the terms: -122.4489796 + 122.4489796 + -2.244897959t + t2 = 0 + 122.4489796 Combine like terms: -122.4489796 + 122.4489796 = 0.0000000 0.0000000 + -2.244897959t + t2 = 0 + 122.4489796 -2.244897959t + t2 = 0 + 122.4489796 Combine like terms: 0 + 122.4489796 = 122.4489796 -2.244897959t + t2 = 122.4489796 The t term is -2.244897959t. Take half its coefficient (-1.12244898). Square it (1.259891713) and add it to both sides. Add '1.259891713' to each side of the equation. -2.244897959t + 1.259891713 + t2 = 122.4489796 + 1.259891713 Reorder the terms: 1.259891713 + -2.244897959t + t2 = 122.4489796 + 1.259891713 Combine like terms: 122.4489796 + 1.259891713 = 123.708871313 1.259891713 + -2.244897959t + t2 = 123.708871313 Factor a perfect square on the left side: (t + -1.12244898)(t + -1.12244898) = 123.708871313 Calculate the square root of the right side: 11.12244898 Break this problem into two subproblems by setting (t + -1.12244898) equal to 11.12244898 and -11.12244898.Subproblem 1
t + -1.12244898 = 11.12244898 Simplifying t + -1.12244898 = 11.12244898 Reorder the terms: -1.12244898 + t = 11.12244898 Solving -1.12244898 + t = 11.12244898 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.12244898' to each side of the equation. -1.12244898 + 1.12244898 + t = 11.12244898 + 1.12244898 Combine like terms: -1.12244898 + 1.12244898 = 0.00000000 0.00000000 + t = 11.12244898 + 1.12244898 t = 11.12244898 + 1.12244898 Combine like terms: 11.12244898 + 1.12244898 = 12.24489796 t = 12.24489796 Simplifying t = 12.24489796Subproblem 2
t + -1.12244898 = -11.12244898 Simplifying t + -1.12244898 = -11.12244898 Reorder the terms: -1.12244898 + t = -11.12244898 Solving -1.12244898 + t = -11.12244898 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.12244898' to each side of the equation. -1.12244898 + 1.12244898 + t = -11.12244898 + 1.12244898 Combine like terms: -1.12244898 + 1.12244898 = 0.00000000 0.00000000 + t = -11.12244898 + 1.12244898 t = -11.12244898 + 1.12244898 Combine like terms: -11.12244898 + 1.12244898 = -10 t = -10 Simplifying t = -10Solution
The solution to the problem is based on the solutions from the subproblems. t = {12.24489796, -10}
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