0=w^2+14w+8

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


Simplifying
0 = w2 + 14w + 8

Reorder the terms:
0 = 8 + 14w + w2

Solving
0 = 8 + 14w + w2

Solving for variable 'w'.

Combine like terms: 0 + -8 = -8
-8 + -14w + -1w2 = 8 + 14w + w2 + -8 + -14w + -1w2

Reorder the terms:
-8 + -14w + -1w2 = 8 + -8 + 14w + -14w + w2 + -1w2

Combine like terms: 8 + -8 = 0
-8 + -14w + -1w2 = 0 + 14w + -14w + w2 + -1w2
-8 + -14w + -1w2 = 14w + -14w + w2 + -1w2

Combine like terms: 14w + -14w = 0
-8 + -14w + -1w2 = 0 + w2 + -1w2
-8 + -14w + -1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
-8 + -14w + -1w2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(8 + 14w + w2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(8 + 14w + w2)' equal to zero and attempt to solve:

Simplifying
8 + 14w + w2 = 0

Solving
8 + 14w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + 14w + -8 + w2 = 0 + -8

Reorder the terms:
8 + -8 + 14w + w2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 14w + w2 = 0 + -8
14w + w2 = 0 + -8

Combine like terms: 0 + -8 = -8
14w + w2 = -8

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

Add '49' to each side of the equation.
14w + 49 + w2 = -8 + 49

Reorder the terms:
49 + 14w + w2 = -8 + 49

Combine like terms: -8 + 49 = 41
49 + 14w + w2 = 41

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

Calculate the square root of the right side: 6.403124237

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


Subproblem 1
w + 7 = 6.403124237

Simplifying
w + 7 = 6.403124237

Reorder the terms:
7 + w = 6.403124237

Solving
7 + w = 6.403124237

Solving for variable 'w'.

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

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

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

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

Simplifying
w = -0.596875763


Subproblem 2
w + 7 = -6.403124237

Simplifying
w + 7 = -6.403124237

Reorder the terms:
7 + w = -6.403124237

Solving
7 + w = -6.403124237

Solving for variable 'w'.

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

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

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

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

Simplifying
w = -13.403124237


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

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