-w^2-4w-5-11w+30+w-42=0

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Solution for -w^2-4w-5-11w+30+w-42=0 equation: 


Simplifying
-1w2 + -4w + -5 + -11w + 30 + w + -42 = 0

Reorder the terms:
-5 + 30 + -42 + -4w + -11w + w + -1w2 = 0

Combine like terms: -5 + 30 = 25
25 + -42 + -4w + -11w + w + -1w2 = 0

Combine like terms: 25 + -42 = -17
-17 + -4w + -11w + w + -1w2 = 0

Combine like terms: -4w + -11w = -15w
-17 + -15w + w + -1w2 = 0

Combine like terms: -15w + w = -14w
-17 + -14w + -1w2 = 0

Solving
-17 + -14w + -1w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(17 + 14w + w2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(17 + 14w + w2)' equal to zero and attempt to solve:

Simplifying
17 + 14w + w2 = 0

Solving
17 + 14w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-17' to each side of the equation.
17 + 14w + -17 + w2 = 0 + -17

Reorder the terms:
17 + -17 + 14w + w2 = 0 + -17

Combine like terms: 17 + -17 = 0
0 + 14w + w2 = 0 + -17
14w + w2 = 0 + -17

Combine like terms: 0 + -17 = -17
14w + w2 = -17

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 = -17 + 49

Reorder the terms:
49 + 14w + w2 = -17 + 49

Combine like terms: -17 + 49 = 32
49 + 14w + w2 = 32

Factor a perfect square on the left side:
(w + 7)(w + 7) = 32

Calculate the square root of the right side: 5.656854249

Break this problem into two subproblems by setting 
(w + 7) equal to 5.656854249 and -5.656854249.


Subproblem 1
w + 7 = 5.656854249

Simplifying
w + 7 = 5.656854249

Reorder the terms:
7 + w = 5.656854249

Solving
7 + w = 5.656854249

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 = 5.656854249 + -7

Combine like terms: 7 + -7 = 0
0 + w = 5.656854249 + -7
w = 5.656854249 + -7

Combine like terms: 5.656854249 + -7 = -1.343145751
w = -1.343145751

Simplifying
w = -1.343145751


Subproblem 2
w + 7 = -5.656854249

Simplifying
w + 7 = -5.656854249

Reorder the terms:
7 + w = -5.656854249

Solving
7 + w = -5.656854249

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 = -5.656854249 + -7

Combine like terms: 7 + -7 = 0
0 + w = -5.656854249 + -7
w = -5.656854249 + -7

Combine like terms: -5.656854249 + -7 = -12.656854249
w = -12.656854249

Simplifying
w = -12.656854249


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {-1.343145751, -12.656854249}
Solution
w = {-1.343145751, -12.656854249}

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