x^2+18x+4=0

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Solution for x^2+18x+4=0 equation: 


Simplifying
x2 + 18x + 4 = 0

Reorder the terms:
4 + 18x + x2 = 0

Solving
4 + 18x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + 18x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + 18x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 18x + x2 = 0 + -4
18x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
18x + x2 = -4

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 = -4 + 81

Reorder the terms:
81 + 18x + x2 = -4 + 81

Combine like terms: -4 + 81 = 77
81 + 18x + x2 = 77

Factor a perfect square on the left side:
(x + 9)(x + 9) = 77

Calculate the square root of the right side: 8.774964387

Break this problem into two subproblems by setting 
(x + 9) equal to 8.774964387 and -8.774964387.


Subproblem 1
x + 9 = 8.774964387

Simplifying
x + 9 = 8.774964387

Reorder the terms:
9 + x = 8.774964387

Solving
9 + x = 8.774964387

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 = 8.774964387 + -9

Combine like terms: 9 + -9 = 0
0 + x = 8.774964387 + -9
x = 8.774964387 + -9

Combine like terms: 8.774964387 + -9 = -0.225035613
x = -0.225035613

Simplifying
x = -0.225035613


Subproblem 2
x + 9 = -8.774964387

Simplifying
x + 9 = -8.774964387

Reorder the terms:
9 + x = -8.774964387

Solving
9 + x = -8.774964387

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 = -8.774964387 + -9

Combine like terms: 9 + -9 = 0
0 + x = -8.774964387 + -9
x = -8.774964387 + -9

Combine like terms: -8.774964387 + -9 = -17.774964387
x = -17.774964387

Simplifying
x = -17.774964387


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.225035613, -17.774964387}

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