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Simplifying n2 = 12n + -7 Reorder the terms: n2 = -7 + 12n Solving n2 = -7 + 12n Solving for variable 'n'. Reorder the terms: 7 + -12n + n2 = -7 + 12n + 7 + -12n Reorder the terms: 7 + -12n + n2 = -7 + 7 + 12n + -12n Combine like terms: -7 + 7 = 0 7 + -12n + n2 = 0 + 12n + -12n 7 + -12n + n2 = 12n + -12n Combine like terms: 12n + -12n = 0 7 + -12n + n2 = 0 Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + -12n + -7 + n2 = 0 + -7 Reorder the terms: 7 + -7 + -12n + n2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -12n + n2 = 0 + -7 -12n + n2 = 0 + -7 Combine like terms: 0 + -7 = -7 -12n + n2 = -7 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 = -7 + 36 Reorder the terms: 36 + -12n + n2 = -7 + 36 Combine like terms: -7 + 36 = 29 36 + -12n + n2 = 29 Factor a perfect square on the left side: (n + -6)(n + -6) = 29 Calculate the square root of the right side: 5.385164807 Break this problem into two subproblems by setting (n + -6) equal to 5.385164807 and -5.385164807.Subproblem 1
n + -6 = 5.385164807 Simplifying n + -6 = 5.385164807 Reorder the terms: -6 + n = 5.385164807 Solving -6 + n = 5.385164807 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 = 5.385164807 + 6 Combine like terms: -6 + 6 = 0 0 + n = 5.385164807 + 6 n = 5.385164807 + 6 Combine like terms: 5.385164807 + 6 = 11.385164807 n = 11.385164807 Simplifying n = 11.385164807Subproblem 2
n + -6 = -5.385164807 Simplifying n + -6 = -5.385164807 Reorder the terms: -6 + n = -5.385164807 Solving -6 + n = -5.385164807 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 = -5.385164807 + 6 Combine like terms: -6 + 6 = 0 0 + n = -5.385164807 + 6 n = -5.385164807 + 6 Combine like terms: -5.385164807 + 6 = 0.614835193 n = 0.614835193 Simplifying n = 0.614835193Solution
The solution to the problem is based on the solutions from the subproblems. n = {11.385164807, 0.614835193}
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