5+5(w+4)w=

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Solution for 5+5(w+4)w= equation: 


Simplifying
5 + 5(w + 4) * w = 0

Reorder the terms:
5 + 5(4 + w) * w = 0

Reorder the terms for easier multiplication:
5 + 5w(4 + w) = 0
5 + (4 * 5w + w * 5w) = 0
5 + (20w + 5w2) = 0

Solving
5 + 20w + 5w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '5'.
5(1 + 4w + w2) = 0

Ignore the factor 5.

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

Simplifying
1 + 4w + w2 = 0

Solving
1 + 4w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 4w + -1 + w2 = 0 + -1

Reorder the terms:
1 + -1 + 4w + w2 = 0 + -1

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

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

The w term is 4w.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4w + 4 + w2 = -1 + 4

Reorder the terms:
4 + 4w + w2 = -1 + 4

Combine like terms: -1 + 4 = 3
4 + 4w + w2 = 3

Factor a perfect square on the left side:
(w + 2)(w + 2) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(w + 2) equal to 1.732050808 and -1.732050808.


Subproblem 1
w + 2 = 1.732050808

Simplifying
w + 2 = 1.732050808

Reorder the terms:
2 + w = 1.732050808

Solving
2 + w = 1.732050808

Solving for variable 'w'.

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

Add '-2' to each side of the equation.
2 + -2 + w = 1.732050808 + -2

Combine like terms: 2 + -2 = 0
0 + w = 1.732050808 + -2
w = 1.732050808 + -2

Combine like terms: 1.732050808 + -2 = -0.267949192
w = -0.267949192

Simplifying
w = -0.267949192


Subproblem 2
w + 2 = -1.732050808

Simplifying
w + 2 = -1.732050808

Reorder the terms:
2 + w = -1.732050808

Solving
2 + w = -1.732050808

Solving for variable 'w'.

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

Add '-2' to each side of the equation.
2 + -2 + w = -1.732050808 + -2

Combine like terms: 2 + -2 = 0
0 + w = -1.732050808 + -2
w = -1.732050808 + -2

Combine like terms: -1.732050808 + -2 = -3.732050808
w = -3.732050808

Simplifying
w = -3.732050808


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {-0.267949192, -3.732050808}
Solution
w = {-0.267949192, -3.732050808}

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