9x^2+123x+4=0

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Solution for 9x^2+123x+4=0 equation: 


Simplifying
9x2 + 123x + 4 = 0

Reorder the terms:
4 + 123x + 9x2 = 0

Solving
4 + 123x + 9x2 = 0

Solving for variable 'x'.

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

Divide each side by '9'.
0.4444444444 + 13.66666667x + x2 = 0

Move the constant term to the right:

Add '-0.4444444444' to each side of the equation.
0.4444444444 + 13.66666667x + -0.4444444444 + x2 = 0 + -0.4444444444

Reorder the terms:
0.4444444444 + -0.4444444444 + 13.66666667x + x2 = 0 + -0.4444444444

Combine like terms: 0.4444444444 + -0.4444444444 = 0.0000000000
0.0000000000 + 13.66666667x + x2 = 0 + -0.4444444444
13.66666667x + x2 = 0 + -0.4444444444

Combine like terms: 0 + -0.4444444444 = -0.4444444444
13.66666667x + x2 = -0.4444444444

The x term is 13.66666667x.  Take half its coefficient (6.833333335).
Square it (46.69444447) and add it to both sides.

Add '46.69444447' to each side of the equation.
13.66666667x + 46.69444447 + x2 = -0.4444444444 + 46.69444447

Reorder the terms:
46.69444447 + 13.66666667x + x2 = -0.4444444444 + 46.69444447

Combine like terms: -0.4444444444 + 46.69444447 = 46.2500000256
46.69444447 + 13.66666667x + x2 = 46.2500000256

Factor a perfect square on the left side:
(x + 6.833333335)(x + 6.833333335) = 46.2500000256

Calculate the square root of the right side: 6.800735256

Break this problem into two subproblems by setting 
(x + 6.833333335) equal to 6.800735256 and -6.800735256.


Subproblem 1
x + 6.833333335 = 6.800735256

Simplifying
x + 6.833333335 = 6.800735256

Reorder the terms:
6.833333335 + x = 6.800735256

Solving
6.833333335 + x = 6.800735256

Solving for variable 'x'.

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

Add '-6.833333335' to each side of the equation.
6.833333335 + -6.833333335 + x = 6.800735256 + -6.833333335

Combine like terms: 6.833333335 + -6.833333335 = 0.000000000
0.000000000 + x = 6.800735256 + -6.833333335
x = 6.800735256 + -6.833333335

Combine like terms: 6.800735256 + -6.833333335 = -0.032598079
x = -0.032598079

Simplifying
x = -0.032598079


Subproblem 2
x + 6.833333335 = -6.800735256

Simplifying
x + 6.833333335 = -6.800735256

Reorder the terms:
6.833333335 + x = -6.800735256

Solving
6.833333335 + x = -6.800735256

Solving for variable 'x'.

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

Add '-6.833333335' to each side of the equation.
6.833333335 + -6.833333335 + x = -6.800735256 + -6.833333335

Combine like terms: 6.833333335 + -6.833333335 = 0.000000000
0.000000000 + x = -6.800735256 + -6.833333335
x = -6.800735256 + -6.833333335

Combine like terms: -6.800735256 + -6.833333335 = -13.634068591
x = -13.634068591

Simplifying
x = -13.634068591


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.032598079, -13.634068591}

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