w^2+14w+39=0

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Solution for w^2+14w+39=0 equation: 


Simplifying
w2 + 14w + 39 = 0

Reorder the terms:
39 + 14w + w2 = 0

Solving
39 + 14w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '-39' to each side of the equation.
39 + 14w + -39 + w2 = 0 + -39

Reorder the terms:
39 + -39 + 14w + w2 = 0 + -39

Combine like terms: 39 + -39 = 0
0 + 14w + w2 = 0 + -39
14w + w2 = 0 + -39

Combine like terms: 0 + -39 = -39
14w + w2 = -39

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 = -39 + 49

Reorder the terms:
49 + 14w + w2 = -39 + 49

Combine like terms: -39 + 49 = 10
49 + 14w + w2 = 10

Factor a perfect square on the left side:
(w + 7)(w + 7) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(w + 7) equal to 3.16227766 and -3.16227766.


Subproblem 1
w + 7 = 3.16227766

Simplifying
w + 7 = 3.16227766

Reorder the terms:
7 + w = 3.16227766

Solving
7 + w = 3.16227766

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 = 3.16227766 + -7

Combine like terms: 7 + -7 = 0
0 + w = 3.16227766 + -7
w = 3.16227766 + -7

Combine like terms: 3.16227766 + -7 = -3.83772234
w = -3.83772234

Simplifying
w = -3.83772234


Subproblem 2
w + 7 = -3.16227766

Simplifying
w + 7 = -3.16227766

Reorder the terms:
7 + w = -3.16227766

Solving
7 + w = -3.16227766

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 = -3.16227766 + -7

Combine like terms: 7 + -7 = 0
0 + w = -3.16227766 + -7
w = -3.16227766 + -7

Combine like terms: -3.16227766 + -7 = -10.16227766
w = -10.16227766

Simplifying
w = -10.16227766


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {-3.83772234, -10.16227766}

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