x^2-14x+2=0

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

Simplifying
x2 + -14x + 2 = 0

Reorder the terms:
2 + -14x + x2 = 0

Solving
2 + -14x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -14x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + -14x + x2 = 0 + -2

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

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

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 = -2 + 49

Reorder the terms:
49 + -14x + x2 = -2 + 49

Combine like terms: -2 + 49 = 47
49 + -14x + x2 = 47

Factor a perfect square on the left side:
(x + -7)(x + -7) = 47

Calculate the square root of the right side: 6.8556546

Break this problem into two subproblems by setting 
(x + -7) equal to 6.8556546 and -6.8556546.

Subproblem 1
x + -7 = 6.8556546

Simplifying
x + -7 = 6.8556546

Reorder the terms:
-7 + x = 6.8556546

Solving
-7 + x = 6.8556546

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 = 6.8556546 + 7

Combine like terms: -7 + 7 = 0
0 + x = 6.8556546 + 7
x = 6.8556546 + 7

Combine like terms: 6.8556546 + 7 = 13.8556546
x = 13.8556546

Simplifying
x = 13.8556546

Subproblem 2
x + -7 = -6.8556546

Simplifying
x + -7 = -6.8556546

Reorder the terms:
-7 + x = -6.8556546

Solving
-7 + x = -6.8556546

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 = -6.8556546 + 7

Combine like terms: -7 + 7 = 0
0 + x = -6.8556546 + 7
x = -6.8556546 + 7

Combine like terms: -6.8556546 + 7 = 0.1443454
x = 0.1443454

Simplifying
x = 0.1443454

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.8556546, 0.1443454}