4x-2-5-3x*(3+51x)-34342423423434x=2

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Solution for 4x-2-5-3x*(3+51x)-34342423423434x=2 equation: 


Simplifying
4x + -2 + -5 + -3x(3 + 51x) + -34342423423434x = 2
4x + -2 + -5 + (3 * -3x + 51x * -3x) + -34342423423434x = 2
4x + -2 + -5 + (-9x + -153x2) + -34342423423434x = 2

Reorder the terms:
-2 + -5 + 4x + -9x + -34342423423434x + -153x2 = 2

Combine like terms: -2 + -5 = -7
-7 + 4x + -9x + -34342423423434x + -153x2 = 2

Combine like terms: 4x + -9x = -5x
-7 + -5x + -34342423423434x + -153x2 = 2

Combine like terms: -5x + -34342423423434x = -34342423423439x
-7 + -34342423423439x + -153x2 = 2

Solving
-7 + -34342423423439x + -153x2 = 2

Solving for variable 'x'.

Reorder the terms:
-7 + -2 + -34342423423439x + -153x2 = 2 + -2

Combine like terms: -7 + -2 = -9
-9 + -34342423423439x + -153x2 = 2 + -2

Combine like terms: 2 + -2 = 0
-9 + -34342423423439x + -153x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(9 + 34342423420000x + 153x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(9 + 34342423420000x + 153x2)' equal to zero and attempt to solve:

Simplifying
9 + 34342423420000x + 153x2 = 0

Solving
9 + 34342423420000x + 153x2 = 0

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

Divide each side by '153'.
0.05882352941 + 224460283800x + x2 = 0

Move the constant term to the right:

Add '-0.05882352941' to each side of the equation.
0.05882352941 + 224460283800x + -0.05882352941 + x2 = 0 + -0.05882352941

Reorder the terms:
0.05882352941 + -0.05882352941 + 224460283800x + x2 = 0 + -0.05882352941

Combine like terms: 0.05882352941 + -0.05882352941 = 0.00000000000
0.00000000000 + 224460283800x + x2 = 0 + -0.05882352941
224460283800x + x2 = 0 + -0.05882352941

Combine like terms: 0 + -0.05882352941 = -0.05882352941
224460283800x + x2 = -0.05882352941

The x term is 224460283800x.  Take half its coefficient (112230141900).
Square it (12595604750000000000000) and add it to both sides.

Add '12595604750000000000000' to each side of the equation.
224460283800x + 12595604750000000000000 + x2 = -0.05882352941 + 12595604750000000000000

Reorder the terms:
12595604750000000000000 + 224460283800x + x2 = -0.05882352941 + 12595604750000000000000

Combine like terms: -0.05882352941 + 12595604750000000000000 = 12595604749999999999999.94117647059
12595604750000000000000 + 224460283800x + x2 = 12595604749999999999999.94117647059

Factor a perfect square on the left side:
(x + 112230141900)(x + 112230141900) = 12595604749999999999999.94117647059

Calculate the square root of the right side: 112230141896.016508601

Break this problem into two subproblems by setting 
(x + 112230141900) equal to 112230141896.016508601 and -112230141896.016508601.


Subproblem 1
x + 112230141900 = 112230141896.016508601

Simplifying
x + 112230141900 = 112230141896.016508601

Reorder the terms:
112230141900 + x = 112230141896.016508601

Solving
112230141900 + x = 112230141896.016508601

Solving for variable 'x'.

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

Add '-112230141900' to each side of the equation.
112230141900 + -112230141900 + x = 112230141896.016508601 + -112230141900

Combine like terms: 112230141900 + -112230141900 = 0
0 + x = 112230141896.016508601 + -112230141900
x = 112230141896.016508601 + -112230141900

Combine like terms: 112230141896.016508601 + -112230141900 = -3.983491399
x = -3.983491399

Simplifying
x = -3.983491399


Subproblem 2
x + 112230141900 = -112230141896.016508601

Simplifying
x + 112230141900 = -112230141896.016508601

Reorder the terms:
112230141900 + x = -112230141896.016508601

Solving
112230141900 + x = -112230141896.016508601

Solving for variable 'x'.

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

Add '-112230141900' to each side of the equation.
112230141900 + -112230141900 + x = -112230141896.016508601 + -112230141900

Combine like terms: 112230141900 + -112230141900 = 0
0 + x = -112230141896.016508601 + -112230141900
x = -112230141896.016508601 + -112230141900

Combine like terms: -112230141896.016508601 + -112230141900 = -224460283796.016508601
x = -224460283796.016508601

Simplifying
x = -224460283796.016508601


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-3.983491399, -224460283796.016508601}
Solution
x = {-3.983491399, -224460283796.016508601}

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