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Simplifying n2 + 12n + 9 = 0 Reorder the terms: 9 + 12n + n2 = 0 Solving 9 + 12n + n2 = 0 Solving for variable 'n'. Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + 12n + -9 + n2 = 0 + -9 Reorder the terms: 9 + -9 + 12n + n2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 12n + n2 = 0 + -9 12n + n2 = 0 + -9 Combine like terms: 0 + -9 = -9 12n + n2 = -9 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 = -9 + 36 Reorder the terms: 36 + 12n + n2 = -9 + 36 Combine like terms: -9 + 36 = 27 36 + 12n + n2 = 27 Factor a perfect square on the left side: (n + 6)(n + 6) = 27 Calculate the square root of the right side: 5.196152423 Break this problem into two subproblems by setting (n + 6) equal to 5.196152423 and -5.196152423.Subproblem 1
n + 6 = 5.196152423 Simplifying n + 6 = 5.196152423 Reorder the terms: 6 + n = 5.196152423 Solving 6 + n = 5.196152423 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 = 5.196152423 + -6 Combine like terms: 6 + -6 = 0 0 + n = 5.196152423 + -6 n = 5.196152423 + -6 Combine like terms: 5.196152423 + -6 = -0.803847577 n = -0.803847577 Simplifying n = -0.803847577Subproblem 2
n + 6 = -5.196152423 Simplifying n + 6 = -5.196152423 Reorder the terms: 6 + n = -5.196152423 Solving 6 + n = -5.196152423 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 = -5.196152423 + -6 Combine like terms: 6 + -6 = 0 0 + n = -5.196152423 + -6 n = -5.196152423 + -6 Combine like terms: -5.196152423 + -6 = -11.196152423 n = -11.196152423 Simplifying n = -11.196152423Solution
The solution to the problem is based on the solutions from the subproblems. n = {-0.803847577, -11.196152423}
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