4x^2+18x+2=0

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


Simplifying
4x2 + 18x + 2 = 0

Reorder the terms:
2 + 18x + 4x2 = 0

Solving
2 + 18x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 9x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(1 + 9x + 2x2)' equal to zero and attempt to solve:

Simplifying
1 + 9x + 2x2 = 0

Solving
1 + 9x + 2x2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
0.5 + 4.5x + x2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + 4.5x + -0.5 + x2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + 4.5x + x2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + 4.5x + x2 = 0 + -0.5
4.5x + x2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
4.5x + x2 = -0.5

The x term is 4.5x.  Take half its coefficient (2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
4.5x + 5.0625 + x2 = -0.5 + 5.0625

Reorder the terms:
5.0625 + 4.5x + x2 = -0.5 + 5.0625

Combine like terms: -0.5 + 5.0625 = 4.5625
5.0625 + 4.5x + x2 = 4.5625

Factor a perfect square on the left side:
(x + 2.25)(x + 2.25) = 4.5625

Calculate the square root of the right side: 2.136000936

Break this problem into two subproblems by setting 
(x + 2.25) equal to 2.136000936 and -2.136000936.


Subproblem 1
x + 2.25 = 2.136000936

Simplifying
x + 2.25 = 2.136000936

Reorder the terms:
2.25 + x = 2.136000936

Solving
2.25 + x = 2.136000936

Solving for variable 'x'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + x = 2.136000936 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + x = 2.136000936 + -2.25
x = 2.136000936 + -2.25

Combine like terms: 2.136000936 + -2.25 = -0.113999064
x = -0.113999064

Simplifying
x = -0.113999064


Subproblem 2
x + 2.25 = -2.136000936

Simplifying
x + 2.25 = -2.136000936

Reorder the terms:
2.25 + x = -2.136000936

Solving
2.25 + x = -2.136000936

Solving for variable 'x'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + x = -2.136000936 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + x = -2.136000936 + -2.25
x = -2.136000936 + -2.25

Combine like terms: -2.136000936 + -2.25 = -4.386000936
x = -4.386000936

Simplifying
x = -4.386000936


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.113999064, -4.386000936}
Solution
x = {-0.113999064, -4.386000936}

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