u^2-12u+34=0

Solution for u^2-12u+34=0 equation:

Simplifying
u2 + -12u + 34 = 0

Reorder the terms:
34 + -12u + u2 = 0

Solving
34 + -12u + u2 = 0

Solving for variable 'u'.

Begin completing the square.

Move the constant term to the right:

Add '-34' to each side of the equation.
34 + -12u + -34 + u2 = 0 + -34

Reorder the terms:
34 + -34 + -12u + u2 = 0 + -34

Combine like terms: 34 + -34 = 0
0 + -12u + u2 = 0 + -34
-12u + u2 = 0 + -34

Combine like terms: 0 + -34 = -34
-12u + u2 = -34

The u term is -12u.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12u + 36 + u2 = -34 + 36

Reorder the terms:
36 + -12u + u2 = -34 + 36

Combine like terms: -34 + 36 = 2
36 + -12u + u2 = 2

Factor a perfect square on the left side:
(u + -6)(u + -6) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(u + -6) equal to 1.414213562 and -1.414213562.

Subproblem 1
u + -6 = 1.414213562

Simplifying
u + -6 = 1.414213562

Reorder the terms:
-6 + u = 1.414213562

Solving
-6 + u = 1.414213562

Solving for variable 'u'.

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

Add '6' to each side of the equation.
-6 + 6 + u = 1.414213562 + 6

Combine like terms: -6 + 6 = 0
0 + u = 1.414213562 + 6
u = 1.414213562 + 6

Combine like terms: 1.414213562 + 6 = 7.414213562
u = 7.414213562

Simplifying
u = 7.414213562

Subproblem 2
u + -6 = -1.414213562

Simplifying
u + -6 = -1.414213562

Reorder the terms:
-6 + u = -1.414213562

Solving
-6 + u = -1.414213562

Solving for variable 'u'.

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

Add '6' to each side of the equation.
-6 + 6 + u = -1.414213562 + 6

Combine like terms: -6 + 6 = 0
0 + u = -1.414213562 + 6
u = -1.414213562 + 6

Combine like terms: -1.414213562 + 6 = 4.585786438
u = 4.585786438

Simplifying
u = 4.585786438

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {7.414213562, 4.585786438}