u^2-14u+3=0

Solution for u^2-14u+3=0 equation:

Simplifying
u2 + -14u + 3 = 0

Reorder the terms:
3 + -14u + u2 = 0

Solving
3 + -14u + u2 = 0

Solving for variable 'u'.

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -14u + -3 + u2 = 0 + -3

Reorder the terms:
3 + -3 + -14u + u2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -14u + u2 = 0 + -3
-14u + u2 = 0 + -3

Combine like terms: 0 + -3 = -3
-14u + u2 = -3

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

Add '49' to each side of the equation.
-14u + 49 + u2 = -3 + 49

Reorder the terms:
49 + -14u + u2 = -3 + 49

Combine like terms: -3 + 49 = 46
49 + -14u + u2 = 46

Factor a perfect square on the left side:
(u + -7)(u + -7) = 46

Calculate the square root of the right side: 6.782329983

Break this problem into two subproblems by setting 
(u + -7) equal to 6.782329983 and -6.782329983.

Subproblem 1
u + -7 = 6.782329983

Simplifying
u + -7 = 6.782329983

Reorder the terms:
-7 + u = 6.782329983

Solving
-7 + u = 6.782329983

Solving for variable 'u'.

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

Add '7' to each side of the equation.
-7 + 7 + u = 6.782329983 + 7

Combine like terms: -7 + 7 = 0
0 + u = 6.782329983 + 7
u = 6.782329983 + 7

Combine like terms: 6.782329983 + 7 = 13.782329983
u = 13.782329983

Simplifying
u = 13.782329983

Subproblem 2
u + -7 = -6.782329983

Simplifying
u + -7 = -6.782329983

Reorder the terms:
-7 + u = -6.782329983

Solving
-7 + u = -6.782329983

Solving for variable 'u'.

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

Add '7' to each side of the equation.
-7 + 7 + u = -6.782329983 + 7

Combine like terms: -7 + 7 = 0
0 + u = -6.782329983 + 7
u = -6.782329983 + 7

Combine like terms: -6.782329983 + 7 = 0.217670017
u = 0.217670017

Simplifying
u = 0.217670017

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {13.782329983, 0.217670017}