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Simplifying 6t2 + -7t + -17 = 0 Reorder the terms: -17 + -7t + 6t2 = 0 Solving -17 + -7t + 6t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -2.833333333 + -1.166666667t + t2 = 0 Move the constant term to the right: Add '2.833333333' to each side of the equation. -2.833333333 + -1.166666667t + 2.833333333 + t2 = 0 + 2.833333333 Reorder the terms: -2.833333333 + 2.833333333 + -1.166666667t + t2 = 0 + 2.833333333 Combine like terms: -2.833333333 + 2.833333333 = 0.000000000 0.000000000 + -1.166666667t + t2 = 0 + 2.833333333 -1.166666667t + t2 = 0 + 2.833333333 Combine like terms: 0 + 2.833333333 = 2.833333333 -1.166666667t + t2 = 2.833333333 The t term is -1.166666667t. Take half its coefficient (-0.5833333335). Square it (0.3402777780) and add it to both sides. Add '0.3402777780' to each side of the equation. -1.166666667t + 0.3402777780 + t2 = 2.833333333 + 0.3402777780 Reorder the terms: 0.3402777780 + -1.166666667t + t2 = 2.833333333 + 0.3402777780 Combine like terms: 2.833333333 + 0.3402777780 = 3.173611111 0.3402777780 + -1.166666667t + t2 = 3.173611111 Factor a perfect square on the left side: (t + -0.5833333335)(t + -0.5833333335) = 3.173611111 Calculate the square root of the right side: 1.781463194 Break this problem into two subproblems by setting (t + -0.5833333335) equal to 1.781463194 and -1.781463194.Subproblem 1
t + -0.5833333335 = 1.781463194 Simplifying t + -0.5833333335 = 1.781463194 Reorder the terms: -0.5833333335 + t = 1.781463194 Solving -0.5833333335 + t = 1.781463194 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5833333335' to each side of the equation. -0.5833333335 + 0.5833333335 + t = 1.781463194 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + t = 1.781463194 + 0.5833333335 t = 1.781463194 + 0.5833333335 Combine like terms: 1.781463194 + 0.5833333335 = 2.3647965275 t = 2.3647965275 Simplifying t = 2.3647965275Subproblem 2
t + -0.5833333335 = -1.781463194 Simplifying t + -0.5833333335 = -1.781463194 Reorder the terms: -0.5833333335 + t = -1.781463194 Solving -0.5833333335 + t = -1.781463194 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5833333335' to each side of the equation. -0.5833333335 + 0.5833333335 + t = -1.781463194 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + t = -1.781463194 + 0.5833333335 t = -1.781463194 + 0.5833333335 Combine like terms: -1.781463194 + 0.5833333335 = -1.1981298605 t = -1.1981298605 Simplifying t = -1.1981298605Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.3647965275, -1.1981298605}
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