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Simplifying 19.8108t2 + -135.22t + 125 = 0 Reorder the terms: 125 + -135.22t + 19.8108t2 = 0 Solving 125 + -135.22t + 19.8108t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 19.8108 the coefficient of the squared term: Divide each side by '19.8108'. 6.309689664 + -6.825569891t + t2 = 0 Move the constant term to the right: Add '-6.309689664' to each side of the equation. 6.309689664 + -6.825569891t + -6.309689664 + t2 = 0 + -6.309689664 Reorder the terms: 6.309689664 + -6.309689664 + -6.825569891t + t2 = 0 + -6.309689664 Combine like terms: 6.309689664 + -6.309689664 = 0.000000000 0.000000000 + -6.825569891t + t2 = 0 + -6.309689664 -6.825569891t + t2 = 0 + -6.309689664 Combine like terms: 0 + -6.309689664 = -6.309689664 -6.825569891t + t2 = -6.309689664 The t term is -6.825569891t. Take half its coefficient (-3.412784946). Square it (11.64710109) and add it to both sides. Add '11.64710109' to each side of the equation. -6.825569891t + 11.64710109 + t2 = -6.309689664 + 11.64710109 Reorder the terms: 11.64710109 + -6.825569891t + t2 = -6.309689664 + 11.64710109 Combine like terms: -6.309689664 + 11.64710109 = 5.337411426 11.64710109 + -6.825569891t + t2 = 5.337411426 Factor a perfect square on the left side: (t + -3.412784946)(t + -3.412784946) = 5.337411426 Calculate the square root of the right side: 2.310283841 Break this problem into two subproblems by setting (t + -3.412784946) equal to 2.310283841 and -2.310283841.Subproblem 1
t + -3.412784946 = 2.310283841 Simplifying t + -3.412784946 = 2.310283841 Reorder the terms: -3.412784946 + t = 2.310283841 Solving -3.412784946 + t = 2.310283841 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.412784946' to each side of the equation. -3.412784946 + 3.412784946 + t = 2.310283841 + 3.412784946 Combine like terms: -3.412784946 + 3.412784946 = 0.000000000 0.000000000 + t = 2.310283841 + 3.412784946 t = 2.310283841 + 3.412784946 Combine like terms: 2.310283841 + 3.412784946 = 5.723068787 t = 5.723068787 Simplifying t = 5.723068787Subproblem 2
t + -3.412784946 = -2.310283841 Simplifying t + -3.412784946 = -2.310283841 Reorder the terms: -3.412784946 + t = -2.310283841 Solving -3.412784946 + t = -2.310283841 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.412784946' to each side of the equation. -3.412784946 + 3.412784946 + t = -2.310283841 + 3.412784946 Combine like terms: -3.412784946 + 3.412784946 = 0.000000000 0.000000000 + t = -2.310283841 + 3.412784946 t = -2.310283841 + 3.412784946 Combine like terms: -2.310283841 + 3.412784946 = 1.102501105 t = 1.102501105 Simplifying t = 1.102501105Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.723068787, 1.102501105}
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