u^2+14u+14=0

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


Simplifying
u2 + 14u + 14 = 0

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

Solving
14 + 14u + u2 = 0

Solving for variable 'u'.

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = -14 + 49

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

Combine like terms: -14 + 49 = 35
49 + 14u + u2 = 35

Factor a perfect square on the left side:
(u + 7)(u + 7) = 35

Calculate the square root of the right side: 5.916079783

Break this problem into two subproblems by setting 
(u + 7) equal to 5.916079783 and -5.916079783.


Subproblem 1
u + 7 = 5.916079783

Simplifying
u + 7 = 5.916079783

Reorder the terms:
7 + u = 5.916079783

Solving
7 + u = 5.916079783

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 = 5.916079783 + -7

Combine like terms: 7 + -7 = 0
0 + u = 5.916079783 + -7
u = 5.916079783 + -7

Combine like terms: 5.916079783 + -7 = -1.083920217
u = -1.083920217

Simplifying
u = -1.083920217


Subproblem 2
u + 7 = -5.916079783

Simplifying
u + 7 = -5.916079783

Reorder the terms:
7 + u = -5.916079783

Solving
7 + u = -5.916079783

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 = -5.916079783 + -7

Combine like terms: 7 + -7 = 0
0 + u = -5.916079783 + -7
u = -5.916079783 + -7

Combine like terms: -5.916079783 + -7 = -12.916079783
u = -12.916079783

Simplifying
u = -12.916079783


Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {-1.083920217, -12.916079783}

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