w^2+11w+22=0

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Solution for w^2+11w+22=0 equation: 


Simplifying
w2 + 11w + 22 = 0

Reorder the terms:
22 + 11w + w2 = 0

Solving
22 + 11w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '-22' to each side of the equation.
22 + 11w + -22 + w2 = 0 + -22

Reorder the terms:
22 + -22 + 11w + w2 = 0 + -22

Combine like terms: 22 + -22 = 0
0 + 11w + w2 = 0 + -22
11w + w2 = 0 + -22

Combine like terms: 0 + -22 = -22
11w + w2 = -22

The w term is 11w.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11w + 30.25 + w2 = -22 + 30.25

Reorder the terms:
30.25 + 11w + w2 = -22 + 30.25

Combine like terms: -22 + 30.25 = 8.25
30.25 + 11w + w2 = 8.25

Factor a perfect square on the left side:
(w + 5.5)(w + 5.5) = 8.25

Calculate the square root of the right side: 2.872281323

Break this problem into two subproblems by setting 
(w + 5.5) equal to 2.872281323 and -2.872281323.


Subproblem 1
w + 5.5 = 2.872281323

Simplifying
w + 5.5 = 2.872281323

Reorder the terms:
5.5 + w = 2.872281323

Solving
5.5 + w = 2.872281323

Solving for variable 'w'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + w = 2.872281323 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + w = 2.872281323 + -5.5
w = 2.872281323 + -5.5

Combine like terms: 2.872281323 + -5.5 = -2.627718677
w = -2.627718677

Simplifying
w = -2.627718677


Subproblem 2
w + 5.5 = -2.872281323

Simplifying
w + 5.5 = -2.872281323

Reorder the terms:
5.5 + w = -2.872281323

Solving
5.5 + w = -2.872281323

Solving for variable 'w'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + w = -2.872281323 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + w = -2.872281323 + -5.5
w = -2.872281323 + -5.5

Combine like terms: -2.872281323 + -5.5 = -8.372281323
w = -8.372281323

Simplifying
w = -8.372281323


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {-2.627718677, -8.372281323}

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