2(x^2-14x+41)=0

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Solution for 2(x^2-14x+41)=0 equation: 


Simplifying
2(x2 + -14x + 41) = 0

Reorder the terms:
2(41 + -14x + x2) = 0
(41 * 2 + -14x * 2 + x2 * 2) = 0
(82 + -28x + 2x2) = 0

Solving
82 + -28x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(41 + -14x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(41 + -14x + x2)' equal to zero and attempt to solve:

Simplifying
41 + -14x + x2 = 0

Solving
41 + -14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-41' to each side of the equation.
41 + -14x + -41 + x2 = 0 + -41

Reorder the terms:
41 + -41 + -14x + x2 = 0 + -41

Combine like terms: 41 + -41 = 0
0 + -14x + x2 = 0 + -41
-14x + x2 = 0 + -41

Combine like terms: 0 + -41 = -41
-14x + x2 = -41

The x term is -14x.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14x + 49 + x2 = -41 + 49

Reorder the terms:
49 + -14x + x2 = -41 + 49

Combine like terms: -41 + 49 = 8
49 + -14x + x2 = 8

Factor a perfect square on the left side:
(x + -7)(x + -7) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(x + -7) equal to 2.828427125 and -2.828427125.


Subproblem 1
x + -7 = 2.828427125

Simplifying
x + -7 = 2.828427125

Reorder the terms:
-7 + x = 2.828427125

Solving
-7 + x = 2.828427125

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = 2.828427125 + 7

Combine like terms: -7 + 7 = 0
0 + x = 2.828427125 + 7
x = 2.828427125 + 7

Combine like terms: 2.828427125 + 7 = 9.828427125
x = 9.828427125

Simplifying
x = 9.828427125


Subproblem 2
x + -7 = -2.828427125

Simplifying
x + -7 = -2.828427125

Reorder the terms:
-7 + x = -2.828427125

Solving
-7 + x = -2.828427125

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = -2.828427125 + 7

Combine like terms: -7 + 7 = 0
0 + x = -2.828427125 + 7
x = -2.828427125 + 7

Combine like terms: -2.828427125 + 7 = 4.171572875
x = 4.171572875

Simplifying
x = 4.171572875


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.828427125, 4.171572875}
Solution
x = {9.828427125, 4.171572875}

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