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Simplifying 600 = 4.9t2 + 8t Reorder the terms: 600 = 8t + 4.9t2 Solving 600 = 8t + 4.9t2 Solving for variable 't'. Reorder the terms: 600 + -8t + -4.9t2 = 8t + -8t + 4.9t2 + -4.9t2 Combine like terms: 8t + -8t = 0 600 + -8t + -4.9t2 = 0 + 4.9t2 + -4.9t2 600 + -8t + -4.9t2 = 4.9t2 + -4.9t2 Combine like terms: 4.9t2 + -4.9t2 = 0.0 600 + -8t + -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 + 1.632653061t + t2 = 0 Move the constant term to the right: Add '122.4489796' to each side of the equation. -122.4489796 + 1.632653061t + 122.4489796 + t2 = 0 + 122.4489796 Reorder the terms: -122.4489796 + 122.4489796 + 1.632653061t + t2 = 0 + 122.4489796 Combine like terms: -122.4489796 + 122.4489796 = 0.0000000 0.0000000 + 1.632653061t + t2 = 0 + 122.4489796 1.632653061t + t2 = 0 + 122.4489796 Combine like terms: 0 + 122.4489796 = 122.4489796 1.632653061t + t2 = 122.4489796 The t term is 1.632653061t. Take half its coefficient (0.8163265305). Square it (0.6663890044) and add it to both sides. Add '0.6663890044' to each side of the equation. 1.632653061t + 0.6663890044 + t2 = 122.4489796 + 0.6663890044 Reorder the terms: 0.6663890044 + 1.632653061t + t2 = 122.4489796 + 0.6663890044 Combine like terms: 122.4489796 + 0.6663890044 = 123.1153686044 0.6663890044 + 1.632653061t + t2 = 123.1153686044 Factor a perfect square on the left side: (t + 0.8163265305)(t + 0.8163265305) = 123.1153686044 Calculate the square root of the right side: 11.095736506 Break this problem into two subproblems by setting (t + 0.8163265305) equal to 11.095736506 and -11.095736506.Subproblem 1
t + 0.8163265305 = 11.095736506 Simplifying t + 0.8163265305 = 11.095736506 Reorder the terms: 0.8163265305 + t = 11.095736506 Solving 0.8163265305 + t = 11.095736506 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.8163265305' to each side of the equation. 0.8163265305 + -0.8163265305 + t = 11.095736506 + -0.8163265305 Combine like terms: 0.8163265305 + -0.8163265305 = 0.0000000000 0.0000000000 + t = 11.095736506 + -0.8163265305 t = 11.095736506 + -0.8163265305 Combine like terms: 11.095736506 + -0.8163265305 = 10.2794099755 t = 10.2794099755 Simplifying t = 10.2794099755Subproblem 2
t + 0.8163265305 = -11.095736506 Simplifying t + 0.8163265305 = -11.095736506 Reorder the terms: 0.8163265305 + t = -11.095736506 Solving 0.8163265305 + t = -11.095736506 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.8163265305' to each side of the equation. 0.8163265305 + -0.8163265305 + t = -11.095736506 + -0.8163265305 Combine like terms: 0.8163265305 + -0.8163265305 = 0.0000000000 0.0000000000 + t = -11.095736506 + -0.8163265305 t = -11.095736506 + -0.8163265305 Combine like terms: -11.095736506 + -0.8163265305 = -11.9120630365 t = -11.9120630365 Simplifying t = -11.9120630365Solution
The solution to the problem is based on the solutions from the subproblems. t = {10.2794099755, -11.9120630365}
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