-4w^2-20w-3=0

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Solution for -4w^2-20w-3=0 equation: 


Simplifying
-4w2 + -20w + -3 = 0

Reorder the terms:
-3 + -20w + -4w2 = 0

Solving
-3 + -20w + -4w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(3 + 20w + 4w2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(3 + 20w + 4w2)' equal to zero and attempt to solve:

Simplifying
3 + 20w + 4w2 = 0

Solving
3 + 20w + 4w2 = 0

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

Divide each side by '4'.
0.75 + 5w + w2 = 0

Move the constant term to the right:

Add '-0.75' to each side of the equation.
0.75 + 5w + -0.75 + w2 = 0 + -0.75

Reorder the terms:
0.75 + -0.75 + 5w + w2 = 0 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + 5w + w2 = 0 + -0.75
5w + w2 = 0 + -0.75

Combine like terms: 0 + -0.75 = -0.75
5w + w2 = -0.75

The w term is 5w.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5w + 6.25 + w2 = -0.75 + 6.25

Reorder the terms:
6.25 + 5w + w2 = -0.75 + 6.25

Combine like terms: -0.75 + 6.25 = 5.5
6.25 + 5w + w2 = 5.5

Factor a perfect square on the left side:
(w + 2.5)(w + 2.5) = 5.5

Calculate the square root of the right side: 2.34520788

Break this problem into two subproblems by setting 
(w + 2.5) equal to 2.34520788 and -2.34520788.


Subproblem 1
w + 2.5 = 2.34520788

Simplifying
w + 2.5 = 2.34520788

Reorder the terms:
2.5 + w = 2.34520788

Solving
2.5 + w = 2.34520788

Solving for variable 'w'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + w = 2.34520788 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + w = 2.34520788 + -2.5
w = 2.34520788 + -2.5

Combine like terms: 2.34520788 + -2.5 = -0.15479212
w = -0.15479212

Simplifying
w = -0.15479212


Subproblem 2
w + 2.5 = -2.34520788

Simplifying
w + 2.5 = -2.34520788

Reorder the terms:
2.5 + w = -2.34520788

Solving
2.5 + w = -2.34520788

Solving for variable 'w'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + w = -2.34520788 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + w = -2.34520788 + -2.5
w = -2.34520788 + -2.5

Combine like terms: -2.34520788 + -2.5 = -4.84520788
w = -4.84520788

Simplifying
w = -4.84520788


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {-0.15479212, -4.84520788}
Solution
w = {-0.15479212, -4.84520788}

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