4w^2+4w-2=0

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Solution for 4w^2+4w-2=0 equation: 


Simplifying
4w2 + 4w + -2 = 0

Reorder the terms:
-2 + 4w + 4w2 = 0

Solving
-2 + 4w + 4w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + 2w + 2w2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-1 + 2w + 2w2)' equal to zero and attempt to solve:

Simplifying
-1 + 2w + 2w2 = 0

Solving
-1 + 2w + 2w2 = 0

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

Divide each side by '2'.
-0.5 + w + w2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + w + 0.5 + w2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + w + w2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + w + w2 = 0 + 0.5
w + w2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
w + w2 = 0.5

The w term is w.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + w2 = 0.5 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + w2 = 0.5 + 0.25

Combine like terms: 0.5 + 0.25 = 0.75
1.25 + w2 = 0.75

Factor a perfect square on the left side:
(w + 0.5)(w + 0.5) = 0.75

Calculate the square root of the right side: 0.866025404

Break this problem into two subproblems by setting 
(w + 0.5) equal to 0.866025404 and -0.866025404.


Subproblem 1
w + 0.5 = 0.866025404

Simplifying
w + 0.5 = 0.866025404

Reorder the terms:
0.5 + w = 0.866025404

Solving
0.5 + w = 0.866025404

Solving for variable 'w'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + w = 0.866025404 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + w = 0.866025404 + -0.5
w = 0.866025404 + -0.5

Combine like terms: 0.866025404 + -0.5 = 0.366025404
w = 0.366025404

Simplifying
w = 0.366025404


Subproblem 2
w + 0.5 = -0.866025404

Simplifying
w + 0.5 = -0.866025404

Reorder the terms:
0.5 + w = -0.866025404

Solving
0.5 + w = -0.866025404

Solving for variable 'w'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + w = -0.866025404 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + w = -0.866025404 + -0.5
w = -0.866025404 + -0.5

Combine like terms: -0.866025404 + -0.5 = -1.366025404
w = -1.366025404

Simplifying
w = -1.366025404


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {0.366025404, -1.366025404}
Solution
w = {0.366025404, -1.366025404}

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