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Simplifying 29t2 + -5850t + 290058 = 0 Reorder the terms: 290058 + -5850t + 29t2 = 0 Solving 290058 + -5850t + 29t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 29 the coefficient of the squared term: Divide each side by '29'. 10002 + -201.7241379t + t2 = 0 Move the constant term to the right: Add '-10002' to each side of the equation. 10002 + -201.7241379t + -10002 + t2 = 0 + -10002 Reorder the terms: 10002 + -10002 + -201.7241379t + t2 = 0 + -10002 Combine like terms: 10002 + -10002 = 0 0 + -201.7241379t + t2 = 0 + -10002 -201.7241379t + t2 = 0 + -10002 Combine like terms: 0 + -10002 = -10002 -201.7241379t + t2 = -10002 The t term is -201.7241379t. Take half its coefficient (-100.862069). Square it (10173.15696) and add it to both sides. Add '10173.15696' to each side of the equation. -201.7241379t + 10173.15696 + t2 = -10002 + 10173.15696 Reorder the terms: 10173.15696 + -201.7241379t + t2 = -10002 + 10173.15696 Combine like terms: -10002 + 10173.15696 = 171.15696 10173.15696 + -201.7241379t + t2 = 171.15696 Factor a perfect square on the left side: (t + -100.862069)(t + -100.862069) = 171.15696 Calculate the square root of the right side: 13.08269697 Break this problem into two subproblems by setting (t + -100.862069) equal to 13.08269697 and -13.08269697.Subproblem 1
t + -100.862069 = 13.08269697 Simplifying t + -100.862069 = 13.08269697 Reorder the terms: -100.862069 + t = 13.08269697 Solving -100.862069 + t = 13.08269697 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '100.862069' to each side of the equation. -100.862069 + 100.862069 + t = 13.08269697 + 100.862069 Combine like terms: -100.862069 + 100.862069 = 0.000000 0.000000 + t = 13.08269697 + 100.862069 t = 13.08269697 + 100.862069 Combine like terms: 13.08269697 + 100.862069 = 113.94476597 t = 113.94476597 Simplifying t = 113.94476597Subproblem 2
t + -100.862069 = -13.08269697 Simplifying t + -100.862069 = -13.08269697 Reorder the terms: -100.862069 + t = -13.08269697 Solving -100.862069 + t = -13.08269697 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '100.862069' to each side of the equation. -100.862069 + 100.862069 + t = -13.08269697 + 100.862069 Combine like terms: -100.862069 + 100.862069 = 0.000000 0.000000 + t = -13.08269697 + 100.862069 t = -13.08269697 + 100.862069 Combine like terms: -13.08269697 + 100.862069 = 87.77937203 t = 87.77937203 Simplifying t = 87.77937203Solution
The solution to the problem is based on the solutions from the subproblems. t = {113.94476597, 87.77937203}
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