-2u^2-28u+2=0

Solution for -2u^2-28u+2=0 equation:

Simplifying
-2u2 + -28u + 2 = 0

Reorder the terms:
2 + -28u + -2u2 = 0

Solving
2 + -28u + -2u2 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + -14u + -1u2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(1 + -14u + -1u2)' equal to zero and attempt to solve:

Simplifying
1 + -14u + -1u2 = 0

Solving
1 + -14u + -1u2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-1 + 14u + u2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 14u + 1 + u2 = 0 + 1

Reorder the terms:
-1 + 1 + 14u + u2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 14u + u2 = 0 + 1
14u + u2 = 0 + 1

Combine like terms: 0 + 1 = 1
14u + u2 = 1

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 = 1 + 49

Reorder the terms:
49 + 14u + u2 = 1 + 49

Combine like terms: 1 + 49 = 50
49 + 14u + u2 = 50

Factor a perfect square on the left side:
(u + 7)(u + 7) = 50

Calculate the square root of the right side: 7.071067812

Break this problem into two subproblems by setting 
(u + 7) equal to 7.071067812 and -7.071067812.

Subproblem 1
u + 7 = 7.071067812

Simplifying
u + 7 = 7.071067812

Reorder the terms:
7 + u = 7.071067812

Solving
7 + u = 7.071067812

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 = 7.071067812 + -7

Combine like terms: 7 + -7 = 0
0 + u = 7.071067812 + -7
u = 7.071067812 + -7

Combine like terms: 7.071067812 + -7 = 0.071067812
u = 0.071067812

Simplifying
u = 0.071067812

Subproblem 2
u + 7 = -7.071067812

Simplifying
u + 7 = -7.071067812

Reorder the terms:
7 + u = -7.071067812

Solving
7 + u = -7.071067812

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 = -7.071067812 + -7

Combine like terms: 7 + -7 = 0
0 + u = -7.071067812 + -7
u = -7.071067812 + -7

Combine like terms: -7.071067812 + -7 = -14.071067812
u = -14.071067812

Simplifying
u = -14.071067812

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {0.071067812, -14.071067812}
Solution
u = {0.071067812, -14.071067812}