(4x^2)-(4x+2)=0

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Solution for (4x^2)-(4x+2)=0 equation: 


Simplifying
(4x2) + -1(4x + 2) = 0

Reorder the terms:
(4x2) + -1(2 + 4x) = 0
(4x2) + (2 * -1 + 4x * -1) = 0
(4x2) + (-2 + -4x) = 0

Reorder the terms:
-2 + -4x + (4x2) = 0

Solving
-2 + -4x + (4x2) = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + -2x + (2x2)) = 0

Ignore the factor 2.

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

Simplifying
-1 + -2x + (2x2) = 0

Solving
-1 + -2x + (2x2) = 0

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

Divide each side by '2'.
-0.5 + -1x + x2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -1x + 0.5 + x2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -1x + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -1x + x2 = 0 + 0.5
-1x + x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-1x + x2 = 0.5

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 0.5 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 0.5 + 0.25

Combine like terms: 0.5 + 0.25 = 0.75
0.25 + -1x + x2 = 0.75

Factor a perfect square on the left side:
((x) + -0.5)((x) + -0.5) = 0.75

Calculate the square root of the right side: 0.866025404

Break this problem into two subproblems by setting 
((x) + -0.5) equal to 0.866025404 and -0.866025404.


Subproblem 1
(x) + -0.5 = 0.866025404

Simplifying
(x) + -0.5 = 0.866025404
x + -0.5 = 0.866025404

Reorder the terms:
-0.5 + x = 0.866025404

Solving
-0.5 + x = 0.866025404

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = 0.866025404 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 0.866025404 + 0.5
x = 0.866025404 + 0.5

Combine like terms: 0.866025404 + 0.5 = 1.366025404
x = 1.366025404

Simplifying
x = 1.366025404


Subproblem 2
(x) + -0.5 = -0.866025404

Simplifying
(x) + -0.5 = -0.866025404
x + -0.5 = -0.866025404

Reorder the terms:
-0.5 + x = -0.866025404

Solving
-0.5 + x = -0.866025404

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = -0.866025404 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -0.866025404 + 0.5
x = -0.866025404 + 0.5

Combine like terms: -0.866025404 + 0.5 = -0.366025404
x = -0.366025404

Simplifying
x = -0.366025404


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.366025404, -0.366025404}
Solution
x = {1.366025404, -0.366025404}

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