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Simplifying 0.83t2 + -6t + 5 = 0 Reorder the terms: 5 + -6t + 0.83t2 = 0 Solving 5 + -6t + 0.83t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 0.83 the coefficient of the squared term: Divide each side by '0.83'. 6.024096386 + -7.228915663t + t2 = 0 Move the constant term to the right: Add '-6.024096386' to each side of the equation. 6.024096386 + -7.228915663t + -6.024096386 + t2 = 0 + -6.024096386 Reorder the terms: 6.024096386 + -6.024096386 + -7.228915663t + t2 = 0 + -6.024096386 Combine like terms: 6.024096386 + -6.024096386 = 0.000000000 0.000000000 + -7.228915663t + t2 = 0 + -6.024096386 -7.228915663t + t2 = 0 + -6.024096386 Combine like terms: 0 + -6.024096386 = -6.024096386 -7.228915663t + t2 = -6.024096386 The t term is -7.228915663t. Take half its coefficient (-3.614457832). Square it (13.06430542) and add it to both sides. Add '13.06430542' to each side of the equation. -7.228915663t + 13.06430542 + t2 = -6.024096386 + 13.06430542 Reorder the terms: 13.06430542 + -7.228915663t + t2 = -6.024096386 + 13.06430542 Combine like terms: -6.024096386 + 13.06430542 = 7.040209034 13.06430542 + -7.228915663t + t2 = 7.040209034 Factor a perfect square on the left side: (t + -3.614457832)(t + -3.614457832) = 7.040209034 Calculate the square root of the right side: 2.653339223 Break this problem into two subproblems by setting (t + -3.614457832) equal to 2.653339223 and -2.653339223.Subproblem 1
t + -3.614457832 = 2.653339223 Simplifying t + -3.614457832 = 2.653339223 Reorder the terms: -3.614457832 + t = 2.653339223 Solving -3.614457832 + t = 2.653339223 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.614457832' to each side of the equation. -3.614457832 + 3.614457832 + t = 2.653339223 + 3.614457832 Combine like terms: -3.614457832 + 3.614457832 = 0.000000000 0.000000000 + t = 2.653339223 + 3.614457832 t = 2.653339223 + 3.614457832 Combine like terms: 2.653339223 + 3.614457832 = 6.267797055 t = 6.267797055 Simplifying t = 6.267797055Subproblem 2
t + -3.614457832 = -2.653339223 Simplifying t + -3.614457832 = -2.653339223 Reorder the terms: -3.614457832 + t = -2.653339223 Solving -3.614457832 + t = -2.653339223 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.614457832' to each side of the equation. -3.614457832 + 3.614457832 + t = -2.653339223 + 3.614457832 Combine like terms: -3.614457832 + 3.614457832 = 0.000000000 0.000000000 + t = -2.653339223 + 3.614457832 t = -2.653339223 + 3.614457832 Combine like terms: -2.653339223 + 3.614457832 = 0.961118609 t = 0.961118609 Simplifying t = 0.961118609Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.267797055, 0.961118609}
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