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Simplifying -6n2 + 7n + 12 = 0 Reorder the terms: 12 + 7n + -6n2 = 0 Solving 12 + 7n + -6n2 = 0 Solving for variable 'n'. Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -2 + -1.166666667n + n2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -1.166666667n + 2 + n2 = 0 + 2 Reorder the terms: -2 + 2 + -1.166666667n + n2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1.166666667n + n2 = 0 + 2 -1.166666667n + n2 = 0 + 2 Combine like terms: 0 + 2 = 2 -1.166666667n + n2 = 2 The n term is -1.166666667n. 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. -1.166666667n + 0.3402777780 + n2 = 2 + 0.3402777780 Reorder the terms: 0.3402777780 + -1.166666667n + n2 = 2 + 0.3402777780 Combine like terms: 2 + 0.3402777780 = 2.340277778 0.3402777780 + -1.166666667n + n2 = 2.340277778 Factor a perfect square on the left side: (n + -0.5833333335)(n + -0.5833333335) = 2.340277778 Calculate the square root of the right side: 1.529796646 Break this problem into two subproblems by setting (n + -0.5833333335) equal to 1.529796646 and -1.529796646.Subproblem 1
n + -0.5833333335 = 1.529796646 Simplifying n + -0.5833333335 = 1.529796646 Reorder the terms: -0.5833333335 + n = 1.529796646 Solving -0.5833333335 + n = 1.529796646 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.5833333335' to each side of the equation. -0.5833333335 + 0.5833333335 + n = 1.529796646 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + n = 1.529796646 + 0.5833333335 n = 1.529796646 + 0.5833333335 Combine like terms: 1.529796646 + 0.5833333335 = 2.1131299795 n = 2.1131299795 Simplifying n = 2.1131299795Subproblem 2
n + -0.5833333335 = -1.529796646 Simplifying n + -0.5833333335 = -1.529796646 Reorder the terms: -0.5833333335 + n = -1.529796646 Solving -0.5833333335 + n = -1.529796646 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.5833333335' to each side of the equation. -0.5833333335 + 0.5833333335 + n = -1.529796646 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + n = -1.529796646 + 0.5833333335 n = -1.529796646 + 0.5833333335 Combine like terms: -1.529796646 + 0.5833333335 = -0.9464633125 n = -0.9464633125 Simplifying n = -0.9464633125Solution
The solution to the problem is based on the solutions from the subproblems. n = {2.1131299795, -0.9464633125}
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