w^2+19w+22=0

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Solution for w^2+19w+22=0 equation: 


Simplifying
w2 + 19w + 22 = 0

Reorder the terms:
22 + 19w + w2 = 0

Solving
22 + 19w + 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 + 19w + -22 + w2 = 0 + -22

Reorder the terms:
22 + -22 + 19w + w2 = 0 + -22

Combine like terms: 22 + -22 = 0
0 + 19w + w2 = 0 + -22
19w + w2 = 0 + -22

Combine like terms: 0 + -22 = -22
19w + w2 = -22

The w term is 19w.  Take half its coefficient (9.5).
Square it (90.25) and add it to both sides.

Add '90.25' to each side of the equation.
19w + 90.25 + w2 = -22 + 90.25

Reorder the terms:
90.25 + 19w + w2 = -22 + 90.25

Combine like terms: -22 + 90.25 = 68.25
90.25 + 19w + w2 = 68.25

Factor a perfect square on the left side:
(w + 9.5)(w + 9.5) = 68.25

Calculate the square root of the right side: 8.261355821

Break this problem into two subproblems by setting 
(w + 9.5) equal to 8.261355821 and -8.261355821.


Subproblem 1
w + 9.5 = 8.261355821

Simplifying
w + 9.5 = 8.261355821

Reorder the terms:
9.5 + w = 8.261355821

Solving
9.5 + w = 8.261355821

Solving for variable 'w'.

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

Add '-9.5' to each side of the equation.
9.5 + -9.5 + w = 8.261355821 + -9.5

Combine like terms: 9.5 + -9.5 = 0.0
0.0 + w = 8.261355821 + -9.5
w = 8.261355821 + -9.5

Combine like terms: 8.261355821 + -9.5 = -1.238644179
w = -1.238644179

Simplifying
w = -1.238644179


Subproblem 2
w + 9.5 = -8.261355821

Simplifying
w + 9.5 = -8.261355821

Reorder the terms:
9.5 + w = -8.261355821

Solving
9.5 + w = -8.261355821

Solving for variable 'w'.

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

Add '-9.5' to each side of the equation.
9.5 + -9.5 + w = -8.261355821 + -9.5

Combine like terms: 9.5 + -9.5 = 0.0
0.0 + w = -8.261355821 + -9.5
w = -8.261355821 + -9.5

Combine like terms: -8.261355821 + -9.5 = -17.761355821
w = -17.761355821

Simplifying
w = -17.761355821


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {-1.238644179, -17.761355821}

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