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Simplifying n2 = 12n + -6 Reorder the terms: n2 = -6 + 12n Solving n2 = -6 + 12n Solving for variable 'n'. Reorder the terms: 6 + -12n + n2 = -6 + 12n + 6 + -12n Reorder the terms: 6 + -12n + n2 = -6 + 6 + 12n + -12n Combine like terms: -6 + 6 = 0 6 + -12n + n2 = 0 + 12n + -12n 6 + -12n + n2 = 12n + -12n Combine like terms: 12n + -12n = 0 6 + -12n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + -12n + -6 + n2 = 0 + -6 Reorder the terms: 6 + -6 + -12n + n2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -12n + n2 = 0 + -6 -12n + n2 = 0 + -6 Combine like terms: 0 + -6 = -6 -12n + n2 = -6 The n term is -12n. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12n + 36 + n2 = -6 + 36 Reorder the terms: 36 + -12n + n2 = -6 + 36 Combine like terms: -6 + 36 = 30 36 + -12n + n2 = 30 Factor a perfect square on the left side: (n + -6)(n + -6) = 30 Calculate the square root of the right side: 5.477225575 Break this problem into two subproblems by setting (n + -6) equal to 5.477225575 and -5.477225575.Subproblem 1
n + -6 = 5.477225575 Simplifying n + -6 = 5.477225575 Reorder the terms: -6 + n = 5.477225575 Solving -6 + n = 5.477225575 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + n = 5.477225575 + 6 Combine like terms: -6 + 6 = 0 0 + n = 5.477225575 + 6 n = 5.477225575 + 6 Combine like terms: 5.477225575 + 6 = 11.477225575 n = 11.477225575 Simplifying n = 11.477225575Subproblem 2
n + -6 = -5.477225575 Simplifying n + -6 = -5.477225575 Reorder the terms: -6 + n = -5.477225575 Solving -6 + n = -5.477225575 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + n = -5.477225575 + 6 Combine like terms: -6 + 6 = 0 0 + n = -5.477225575 + 6 n = -5.477225575 + 6 Combine like terms: -5.477225575 + 6 = 0.522774425 n = 0.522774425 Simplifying n = 0.522774425Solution
The solution to the problem is based on the solutions from the subproblems. n = {11.477225575, 0.522774425}
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