4x(x-23)+3(-2)=2

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Solution for 4x(x-23)+3(-2)=2 equation: 


Simplifying
4x(x + -23) + 3(-2) = 2

Reorder the terms:
4x(-23 + x) + 3(-2) = 2
(-23 * 4x + x * 4x) + 3(-2) = 2
(-92x + 4x2) + 3(-2) = 2

Multiply 3 * -2
-92x + 4x2 + -6 = 2

Reorder the terms:
-6 + -92x + 4x2 = 2

Solving
-6 + -92x + 4x2 = 2

Solving for variable 'x'.

Reorder the terms:
-6 + -2 + -92x + 4x2 = 2 + -2

Combine like terms: -6 + -2 = -8
-8 + -92x + 4x2 = 2 + -2

Combine like terms: 2 + -2 = 0
-8 + -92x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-2 + -23x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-2 + -23x + x2)' equal to zero and attempt to solve:

Simplifying
-2 + -23x + x2 = 0

Solving
-2 + -23x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -23x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + -23x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -23x + x2 = 0 + 2
-23x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
-23x + x2 = 2

The x term is -23x.  Take half its coefficient (-11.5).
Square it (132.25) and add it to both sides.

Add '132.25' to each side of the equation.
-23x + 132.25 + x2 = 2 + 132.25

Reorder the terms:
132.25 + -23x + x2 = 2 + 132.25

Combine like terms: 2 + 132.25 = 134.25
132.25 + -23x + x2 = 134.25

Factor a perfect square on the left side:
(x + -11.5)(x + -11.5) = 134.25

Calculate the square root of the right side: 11.586630226

Break this problem into two subproblems by setting 
(x + -11.5) equal to 11.586630226 and -11.586630226.


Subproblem 1
x + -11.5 = 11.586630226

Simplifying
x + -11.5 = 11.586630226

Reorder the terms:
-11.5 + x = 11.586630226

Solving
-11.5 + x = 11.586630226

Solving for variable 'x'.

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

Add '11.5' to each side of the equation.
-11.5 + 11.5 + x = 11.586630226 + 11.5

Combine like terms: -11.5 + 11.5 = 0.0
0.0 + x = 11.586630226 + 11.5
x = 11.586630226 + 11.5

Combine like terms: 11.586630226 + 11.5 = 23.086630226
x = 23.086630226

Simplifying
x = 23.086630226


Subproblem 2
x + -11.5 = -11.586630226

Simplifying
x + -11.5 = -11.586630226

Reorder the terms:
-11.5 + x = -11.586630226

Solving
-11.5 + x = -11.586630226

Solving for variable 'x'.

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

Add '11.5' to each side of the equation.
-11.5 + 11.5 + x = -11.586630226 + 11.5

Combine like terms: -11.5 + 11.5 = 0.0
0.0 + x = -11.586630226 + 11.5
x = -11.586630226 + 11.5

Combine like terms: -11.586630226 + 11.5 = -0.086630226
x = -0.086630226

Simplifying
x = -0.086630226


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {23.086630226, -0.086630226}
Solution
x = {23.086630226, -0.086630226}

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