2(x^2-2x+2)=14

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Solution for 2(x^2-2x+2)=14 equation: 


Simplifying
2(x2 + -2x + 2) = 14

Reorder the terms:
2(2 + -2x + x2) = 14
(2 * 2 + -2x * 2 + x2 * 2) = 14
(4 + -4x + 2x2) = 14

Solving
4 + -4x + 2x2 = 14

Solving for variable 'x'.

Reorder the terms:
4 + -14 + -4x + 2x2 = 14 + -14

Combine like terms: 4 + -14 = -10
-10 + -4x + 2x2 = 14 + -14

Combine like terms: 14 + -14 = 0
-10 + -4x + 2x2 = 0

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

Ignore the factor 2.

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

Simplifying
-5 + -2x + x2 = 0

Solving
-5 + -2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -2x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + -2x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2x + x2 = 0 + 5
-2x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
-2x + x2 = 5

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 5 + 1

Reorder the terms:
1 + -2x + x2 = 5 + 1

Combine like terms: 5 + 1 = 6
1 + -2x + x2 = 6

Factor a perfect square on the left side:
(x + -1)(x + -1) = 6

Calculate the square root of the right side: 2.449489743

Break this problem into two subproblems by setting 
(x + -1) equal to 2.449489743 and -2.449489743.


Subproblem 1
x + -1 = 2.449489743

Simplifying
x + -1 = 2.449489743

Reorder the terms:
-1 + x = 2.449489743

Solving
-1 + x = 2.449489743

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 2.449489743 + 1

Combine like terms: -1 + 1 = 0
0 + x = 2.449489743 + 1
x = 2.449489743 + 1

Combine like terms: 2.449489743 + 1 = 3.449489743
x = 3.449489743

Simplifying
x = 3.449489743


Subproblem 2
x + -1 = -2.449489743

Simplifying
x + -1 = -2.449489743

Reorder the terms:
-1 + x = -2.449489743

Solving
-1 + x = -2.449489743

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -2.449489743 + 1

Combine like terms: -1 + 1 = 0
0 + x = -2.449489743 + 1
x = -2.449489743 + 1

Combine like terms: -2.449489743 + 1 = -1.449489743
x = -1.449489743

Simplifying
x = -1.449489743


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.449489743, -1.449489743}
Solution
x = {3.449489743, -1.449489743}

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