4x^2-4x+4=14

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Solution for 4x^2-4x+4=14 equation: 


Simplifying
4x2 + -4x + 4 = 14

Reorder the terms:
4 + -4x + 4x2 = 14

Solving
4 + -4x + 4x2 = 14

Solving for variable 'x'.

Reorder the terms:
4 + -14 + -4x + 4x2 = 14 + -14

Combine like terms: 4 + -14 = -10
-10 + -4x + 4x2 = 14 + -14

Combine like terms: 14 + -14 = 0
-10 + -4x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -2x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-5 + -2x + 2x2)' equal to zero and attempt to solve:

Simplifying
-5 + -2x + 2x2 = 0

Solving
-5 + -2x + 2x2 = 0

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

Divide each side by '2'.
-2.5 + -1x + x2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + -1x + 2.5 + x2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + -1x + x2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + -1x + x2 = 0 + 2.5
-1x + x2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
-1x + x2 = 2.5

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 = 2.5 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 2.5 + 0.25

Combine like terms: 2.5 + 0.25 = 2.75
0.25 + -1x + x2 = 2.75

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 2.75

Calculate the square root of the right side: 1.658312395

Break this problem into two subproblems by setting 
(x + -0.5) equal to 1.658312395 and -1.658312395.


Subproblem 1
x + -0.5 = 1.658312395

Simplifying
x + -0.5 = 1.658312395

Reorder the terms:
-0.5 + x = 1.658312395

Solving
-0.5 + x = 1.658312395

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 = 1.658312395 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 1.658312395 + 0.5
x = 1.658312395 + 0.5

Combine like terms: 1.658312395 + 0.5 = 2.158312395
x = 2.158312395

Simplifying
x = 2.158312395


Subproblem 2
x + -0.5 = -1.658312395

Simplifying
x + -0.5 = -1.658312395

Reorder the terms:
-0.5 + x = -1.658312395

Solving
-0.5 + x = -1.658312395

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 = -1.658312395 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -1.658312395 + 0.5
x = -1.658312395 + 0.5

Combine like terms: -1.658312395 + 0.5 = -1.158312395
x = -1.158312395

Simplifying
x = -1.158312395


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.158312395, -1.158312395}
Solution
x = {2.158312395, -1.158312395}

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