324x^2+162x+2=0

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Solution for 324x^2+162x+2=0 equation: 


Simplifying
324x2 + 162x + 2 = 0

Reorder the terms:
2 + 162x + 324x2 = 0

Solving
2 + 162x + 324x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 81x + 162x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(1 + 81x + 162x2)' equal to zero and attempt to solve:

Simplifying
1 + 81x + 162x2 = 0

Solving
1 + 81x + 162x2 = 0

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

Divide each side by '162'.
0.006172839506 + 0.5x + x2 = 0

Move the constant term to the right:

Add '-0.006172839506' to each side of the equation.
0.006172839506 + 0.5x + -0.006172839506 + x2 = 0 + -0.006172839506

Reorder the terms:
0.006172839506 + -0.006172839506 + 0.5x + x2 = 0 + -0.006172839506

Combine like terms: 0.006172839506 + -0.006172839506 = 0.000000000000
0.000000000000 + 0.5x + x2 = 0 + -0.006172839506
0.5x + x2 = 0 + -0.006172839506

Combine like terms: 0 + -0.006172839506 = -0.006172839506
0.5x + x2 = -0.006172839506

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = -0.006172839506 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = -0.006172839506 + 0.0625

Combine like terms: -0.006172839506 + 0.0625 = 0.056327160494
0.0625 + 0.5x + x2 = 0.056327160494

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 0.056327160494

Calculate the square root of the right side: 0.237333437

Break this problem into two subproblems by setting 
(x + 0.25) equal to 0.237333437 and -0.237333437.


Subproblem 1
x + 0.25 = 0.237333437

Simplifying
x + 0.25 = 0.237333437

Reorder the terms:
0.25 + x = 0.237333437

Solving
0.25 + x = 0.237333437

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = 0.237333437 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = 0.237333437 + -0.25
x = 0.237333437 + -0.25

Combine like terms: 0.237333437 + -0.25 = -0.012666563
x = -0.012666563

Simplifying
x = -0.012666563


Subproblem 2
x + 0.25 = -0.237333437

Simplifying
x + 0.25 = -0.237333437

Reorder the terms:
0.25 + x = -0.237333437

Solving
0.25 + x = -0.237333437

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = -0.237333437 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = -0.237333437 + -0.25
x = -0.237333437 + -0.25

Combine like terms: -0.237333437 + -0.25 = -0.487333437
x = -0.487333437

Simplifying
x = -0.487333437


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.012666563, -0.487333437}
Solution
x = {-0.012666563, -0.487333437}

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