b^2+14b+8=0

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Solution for b^2+14b+8=0 equation: 


Simplifying
b2 + 14b + 8 = 0

Reorder the terms:
8 + 14b + b2 = 0

Solving
8 + 14b + b2 = 0

Solving for variable 'b'.

Begin completing the square.

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + 14b + -8 + b2 = 0 + -8

Reorder the terms:
8 + -8 + 14b + b2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 14b + b2 = 0 + -8
14b + b2 = 0 + -8

Combine like terms: 0 + -8 = -8
14b + b2 = -8

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

Add '49' to each side of the equation.
14b + 49 + b2 = -8 + 49

Reorder the terms:
49 + 14b + b2 = -8 + 49

Combine like terms: -8 + 49 = 41
49 + 14b + b2 = 41

Factor a perfect square on the left side:
(b + 7)(b + 7) = 41

Calculate the square root of the right side: 6.403124237

Break this problem into two subproblems by setting 
(b + 7) equal to 6.403124237 and -6.403124237.


Subproblem 1
b + 7 = 6.403124237

Simplifying
b + 7 = 6.403124237

Reorder the terms:
7 + b = 6.403124237

Solving
7 + b = 6.403124237

Solving for variable 'b'.

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

Add '-7' to each side of the equation.
7 + -7 + b = 6.403124237 + -7

Combine like terms: 7 + -7 = 0
0 + b = 6.403124237 + -7
b = 6.403124237 + -7

Combine like terms: 6.403124237 + -7 = -0.596875763
b = -0.596875763

Simplifying
b = -0.596875763


Subproblem 2
b + 7 = -6.403124237

Simplifying
b + 7 = -6.403124237

Reorder the terms:
7 + b = -6.403124237

Solving
7 + b = -6.403124237

Solving for variable 'b'.

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

Add '-7' to each side of the equation.
7 + -7 + b = -6.403124237 + -7

Combine like terms: 7 + -7 = 0
0 + b = -6.403124237 + -7
b = -6.403124237 + -7

Combine like terms: -6.403124237 + -7 = -13.403124237
b = -13.403124237

Simplifying
b = -13.403124237


Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {-0.596875763, -13.403124237}

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