n^2+12n+9=0

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Solution for n^2+12n+9=0 equation:


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 = -0.803847577

Subproblem 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 = -11.196152423

Solution

The solution to the problem is based on the solutions from the subproblems. n = {-0.803847577, -11.196152423}

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