-8w^2-14w-1=0

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Solution for -8w^2-14w-1=0 equation: 


Simplifying
-8w2 + -14w + -1 = 0

Reorder the terms:
-1 + -14w + -8w2 = 0

Solving
-1 + -14w + -8w2 = 0

Solving for variable 'w'.

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

Ignore the factor -1.

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

Simplifying
1 + 14w + 8w2 = 0

Solving
1 + 14w + 8w2 = 0

Begin completing the square.  Divide all terms by
8 the coefficient of the squared term: 

Divide each side by '8'.
0.125 + 1.75w + w2 = 0

Move the constant term to the right:

Add '-0.125' to each side of the equation.
0.125 + 1.75w + -0.125 + w2 = 0 + -0.125

Reorder the terms:
0.125 + -0.125 + 1.75w + w2 = 0 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + 1.75w + w2 = 0 + -0.125
1.75w + w2 = 0 + -0.125

Combine like terms: 0 + -0.125 = -0.125
1.75w + w2 = -0.125

The w term is 1.75w.  Take half its coefficient (0.875).
Square it (0.765625) and add it to both sides.

Add '0.765625' to each side of the equation.
1.75w + 0.765625 + w2 = -0.125 + 0.765625

Reorder the terms:
0.765625 + 1.75w + w2 = -0.125 + 0.765625

Combine like terms: -0.125 + 0.765625 = 0.640625
0.765625 + 1.75w + w2 = 0.640625

Factor a perfect square on the left side:
(w + 0.875)(w + 0.875) = 0.640625

Calculate the square root of the right side: 0.80039053

Break this problem into two subproblems by setting 
(w + 0.875) equal to 0.80039053 and -0.80039053.


Subproblem 1
w + 0.875 = 0.80039053

Simplifying
w + 0.875 = 0.80039053

Reorder the terms:
0.875 + w = 0.80039053

Solving
0.875 + w = 0.80039053

Solving for variable 'w'.

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

Add '-0.875' to each side of the equation.
0.875 + -0.875 + w = 0.80039053 + -0.875

Combine like terms: 0.875 + -0.875 = 0.000
0.000 + w = 0.80039053 + -0.875
w = 0.80039053 + -0.875

Combine like terms: 0.80039053 + -0.875 = -0.07460947
w = -0.07460947

Simplifying
w = -0.07460947


Subproblem 2
w + 0.875 = -0.80039053

Simplifying
w + 0.875 = -0.80039053

Reorder the terms:
0.875 + w = -0.80039053

Solving
0.875 + w = -0.80039053

Solving for variable 'w'.

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

Add '-0.875' to each side of the equation.
0.875 + -0.875 + w = -0.80039053 + -0.875

Combine like terms: 0.875 + -0.875 = 0.000
0.000 + w = -0.80039053 + -0.875
w = -0.80039053 + -0.875

Combine like terms: -0.80039053 + -0.875 = -1.67539053
w = -1.67539053

Simplifying
w = -1.67539053


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {-0.07460947, -1.67539053}
Solution
w = {-0.07460947, -1.67539053}

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