(w+4)=2w^2+11w+6

Solution for (w+4)=2w^2+11w+6 equation:

Simplifying
(w + 4) = 2w2 + 11w + 6

Reorder the terms:
(4 + w) = 2w2 + 11w + 6

Remove parenthesis around (4 + w)
4 + w = 2w2 + 11w + 6

Reorder the terms:
4 + w = 6 + 11w + 2w2

Solving
4 + w = 6 + 11w + 2w2

Solving for variable 'w'.

Reorder the terms:
4 + -6 + w + -11w + -2w2 = 6 + 11w + 2w2 + -6 + -11w + -2w2

Combine like terms: 4 + -6 = -2
-2 + w + -11w + -2w2 = 6 + 11w + 2w2 + -6 + -11w + -2w2

Combine like terms: w + -11w = -10w
-2 + -10w + -2w2 = 6 + 11w + 2w2 + -6 + -11w + -2w2

Reorder the terms:
-2 + -10w + -2w2 = 6 + -6 + 11w + -11w + 2w2 + -2w2

Combine like terms: 6 + -6 = 0
-2 + -10w + -2w2 = 0 + 11w + -11w + 2w2 + -2w2
-2 + -10w + -2w2 = 11w + -11w + 2w2 + -2w2

Combine like terms: 11w + -11w = 0
-2 + -10w + -2w2 = 0 + 2w2 + -2w2
-2 + -10w + -2w2 = 2w2 + -2w2

Combine like terms: 2w2 + -2w2 = 0
-2 + -10w + -2w2 = 0

Factor out the Greatest Common Factor (GCF), '-2'.
-2(1 + 5w + w2) = 0

Ignore the factor -2.
Subproblem 1
Set the factor '(1 + 5w + w2)' equal to zero and attempt to solve:

Simplifying
1 + 5w + w2 = 0

Solving
1 + 5w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 5w + -1 + w2 = 0 + -1

Reorder the terms:
1 + -1 + 5w + w2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 5w + w2 = 0 + -1
5w + w2 = 0 + -1

Combine like terms: 0 + -1 = -1
5w + w2 = -1

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 = -1 + 6.25

Reorder the terms:
6.25 + 5w + w2 = -1 + 6.25

Combine like terms: -1 + 6.25 = 5.25
6.25 + 5w + w2 = 5.25

Factor a perfect square on the left side:
(w + 2.5)(w + 2.5) = 5.25

Calculate the square root of the right side: 2.291287847

Break this problem into two subproblems by setting 
(w + 2.5) equal to 2.291287847 and -2.291287847.

Subproblem 1
w + 2.5 = 2.291287847

Simplifying
w + 2.5 = 2.291287847

Reorder the terms:
2.5 + w = 2.291287847

Solving
2.5 + w = 2.291287847

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 = 2.291287847 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + w = 2.291287847 + -2.5
w = 2.291287847 + -2.5

Combine like terms: 2.291287847 + -2.5 = -0.208712153
w = -0.208712153

Simplifying
w = -0.208712153

Subproblem 2
w + 2.5 = -2.291287847

Simplifying
w + 2.5 = -2.291287847

Reorder the terms:
2.5 + w = -2.291287847

Solving
2.5 + w = -2.291287847

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 = -2.291287847 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + w = -2.291287847 + -2.5
w = -2.291287847 + -2.5

Combine like terms: -2.291287847 + -2.5 = -4.791287847
w = -4.791287847

Simplifying
w = -4.791287847

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {-0.208712153, -4.791287847}
Solution
w = {-0.208712153, -4.791287847}