324x^2+81x+4=0

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Solution for 324x^2+81x+4=0 equation: 


Simplifying
324x2 + 81x + 4 = 0

Reorder the terms:
4 + 81x + 324x2 = 0

Solving
4 + 81x + 324x2 = 0

Solving for variable 'x'.

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

Divide each side by '324'.
0.01234567901 + 0.25x + x2 = 0

Move the constant term to the right:

Add '-0.01234567901' to each side of the equation.
0.01234567901 + 0.25x + -0.01234567901 + x2 = 0 + -0.01234567901

Reorder the terms:
0.01234567901 + -0.01234567901 + 0.25x + x2 = 0 + -0.01234567901

Combine like terms: 0.01234567901 + -0.01234567901 = 0.00000000000
0.00000000000 + 0.25x + x2 = 0 + -0.01234567901
0.25x + x2 = 0 + -0.01234567901

Combine like terms: 0 + -0.01234567901 = -0.01234567901
0.25x + x2 = -0.01234567901

The x term is 0.25x.  Take half its coefficient (0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
0.25x + 0.015625 + x2 = -0.01234567901 + 0.015625

Reorder the terms:
0.015625 + 0.25x + x2 = -0.01234567901 + 0.015625

Combine like terms: -0.01234567901 + 0.015625 = 0.00327932099
0.015625 + 0.25x + x2 = 0.00327932099

Factor a perfect square on the left side:
(x + 0.125)(x + 0.125) = 0.00327932099

Calculate the square root of the right side: 0.057265356

Break this problem into two subproblems by setting 
(x + 0.125) equal to 0.057265356 and -0.057265356.


Subproblem 1
x + 0.125 = 0.057265356

Simplifying
x + 0.125 = 0.057265356

Reorder the terms:
0.125 + x = 0.057265356

Solving
0.125 + x = 0.057265356

Solving for variable 'x'.

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

Add '-0.125' to each side of the equation.
0.125 + -0.125 + x = 0.057265356 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + x = 0.057265356 + -0.125
x = 0.057265356 + -0.125

Combine like terms: 0.057265356 + -0.125 = -0.067734644
x = -0.067734644

Simplifying
x = -0.067734644


Subproblem 2
x + 0.125 = -0.057265356

Simplifying
x + 0.125 = -0.057265356

Reorder the terms:
0.125 + x = -0.057265356

Solving
0.125 + x = -0.057265356

Solving for variable 'x'.

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

Add '-0.125' to each side of the equation.
0.125 + -0.125 + x = -0.057265356 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + x = -0.057265356 + -0.125
x = -0.057265356 + -0.125

Combine like terms: -0.057265356 + -0.125 = -0.182265356
x = -0.182265356

Simplifying
x = -0.182265356


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.067734644, -0.182265356}

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