x^2+18x+11=0

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Solution for x^2+18x+11=0 equation: 


Simplifying
x2 + 18x + 11 = 0

Reorder the terms:
11 + 18x + x2 = 0

Solving
11 + 18x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-11' to each side of the equation.
11 + 18x + -11 + x2 = 0 + -11

Reorder the terms:
11 + -11 + 18x + x2 = 0 + -11

Combine like terms: 11 + -11 = 0
0 + 18x + x2 = 0 + -11
18x + x2 = 0 + -11

Combine like terms: 0 + -11 = -11
18x + x2 = -11

The x term is 18x.  Take half its coefficient (9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
18x + 81 + x2 = -11 + 81

Reorder the terms:
81 + 18x + x2 = -11 + 81

Combine like terms: -11 + 81 = 70
81 + 18x + x2 = 70

Factor a perfect square on the left side:
(x + 9)(x + 9) = 70

Calculate the square root of the right side: 8.366600265

Break this problem into two subproblems by setting 
(x + 9) equal to 8.366600265 and -8.366600265.


Subproblem 1
x + 9 = 8.366600265

Simplifying
x + 9 = 8.366600265

Reorder the terms:
9 + x = 8.366600265

Solving
9 + x = 8.366600265

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-9' to each side of the equation.
9 + -9 + x = 8.366600265 + -9

Combine like terms: 9 + -9 = 0
0 + x = 8.366600265 + -9
x = 8.366600265 + -9

Combine like terms: 8.366600265 + -9 = -0.633399735
x = -0.633399735

Simplifying
x = -0.633399735


Subproblem 2
x + 9 = -8.366600265

Simplifying
x + 9 = -8.366600265

Reorder the terms:
9 + x = -8.366600265

Solving
9 + x = -8.366600265

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-9' to each side of the equation.
9 + -9 + x = -8.366600265 + -9

Combine like terms: 9 + -9 = 0
0 + x = -8.366600265 + -9
x = -8.366600265 + -9

Combine like terms: -8.366600265 + -9 = -17.366600265
x = -17.366600265

Simplifying
x = -17.366600265


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.633399735, -17.366600265}

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