2344-2355x(66478+6678x)=5677-567x

Solution for 2344-2355x(66478+6678x)=5677-567x equation:

Simplifying
2344 + -2355x(66478 + 6678x) = 5677 + -567x
2344 + (66478 * -2355x + 6678x * -2355x) = 5677 + -567x
2344 + (-156555690x + -15726690x2) = 5677 + -567x

Solving
2344 + -156555690x + -15726690x2 = 5677 + -567x

Solving for variable 'x'.

Reorder the terms:
2344 + -5677 + -156555690x + 567x + -15726690x2 = 5677 + -567x + -5677 + 567x

Combine like terms: 2344 + -5677 = -3333
-3333 + -156555690x + 567x + -15726690x2 = 5677 + -567x + -5677 + 567x

Combine like terms: -156555690x + 567x = -156555123x
-3333 + -156555123x + -15726690x2 = 5677 + -567x + -5677 + 567x

Reorder the terms:
-3333 + -156555123x + -15726690x2 = 5677 + -5677 + -567x + 567x

Combine like terms: 5677 + -5677 = 0
-3333 + -156555123x + -15726690x2 = 0 + -567x + 567x
-3333 + -156555123x + -15726690x2 = -567x + 567x

Combine like terms: -567x + 567x = 0
-3333 + -156555123x + -15726690x2 = 0

Factor out the Greatest Common Factor (GCF), '-3'.
-3(1111 + 52185041x + 5242230x2) = 0

Ignore the factor -3.
Subproblem 1
Set the factor '(1111 + 52185041x + 5242230x2)' equal to zero and attempt to solve:

Simplifying
1111 + 52185041x + 5242230x2 = 0

Solving
1111 + 52185041x + 5242230x2 = 0

Begin completing the square.  Divide all terms by
5242230 the coefficient of the squared term: 

Divide each side by '5242230'.
0.000211932708 + 9.954740826x + x2 = 0.0

Move the constant term to the right:

Add '-0.000211932708' to each side of the equation.
0.000211932708 + 9.954740826x + -0.000211932708 + x2 = 0.0 + -0.000211932708

Reorder the terms:
0.000211932708 + -0.000211932708 + 9.954740826x + x2 = 0.0 + -0.000211932708

Combine like terms: 0.000211932708 + -0.000211932708 = 0.000000000000
0.000000000000 + 9.954740826x + x2 = 0.0 + -0.000211932708
9.954740826x + x2 = 0.0 + -0.000211932708

Combine like terms: 0.0 + -0.000211932708 = -0.000211932708
9.954740826x + x2 = -0.000211932708

The x term is 9.954740826x.  Take half its coefficient (4.977370413).
Square it (24.77421623) and add it to both sides.

Add '24.77421623' to each side of the equation.
9.954740826x + 24.77421623 + x2 = -0.000211932708 + 24.77421623

Reorder the terms:
24.77421623 + 9.954740826x + x2 = -0.000211932708 + 24.77421623

Combine like terms: -0.000211932708 + 24.77421623 = 24.774004297292
24.77421623 + 9.954740826x + x2 = 24.774004297292

Factor a perfect square on the left side:
(x + 4.977370413)(x + 4.977370413) = 24.774004297292

Calculate the square root of the right side: 4.977349124

Break this problem into two subproblems by setting 
(x + 4.977370413) equal to 4.977349124 and -4.977349124.

Subproblem 1
x + 4.977370413 = 4.977349124

Simplifying
x + 4.977370413 = 4.977349124

Reorder the terms:
4.977370413 + x = 4.977349124

Solving
4.977370413 + x = 4.977349124

Solving for variable 'x'.

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

Add '-4.977370413' to each side of the equation.
4.977370413 + -4.977370413 + x = 4.977349124 + -4.977370413

Combine like terms: 4.977370413 + -4.977370413 = 0.000000000
0.000000000 + x = 4.977349124 + -4.977370413
x = 4.977349124 + -4.977370413

Combine like terms: 4.977349124 + -4.977370413 = -0.000021289
x = -0.000021289

Simplifying
x = -0.000021289

Subproblem 2
x + 4.977370413 = -4.977349124

Simplifying
x + 4.977370413 = -4.977349124

Reorder the terms:
4.977370413 + x = -4.977349124

Solving
4.977370413 + x = -4.977349124

Solving for variable 'x'.

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

Add '-4.977370413' to each side of the equation.
4.977370413 + -4.977370413 + x = -4.977349124 + -4.977370413

Combine like terms: 4.977370413 + -4.977370413 = 0.000000000
0.000000000 + x = -4.977349124 + -4.977370413
x = -4.977349124 + -4.977370413

Combine like terms: -4.977349124 + -4.977370413 = -9.954719537
x = -9.954719537

Simplifying
x = -9.954719537

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.000021289, -9.954719537}
Solution
x = {-0.000021289, -9.954719537}