x^2+19x+44=0

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Solution for x^2+19x+44=0 equation: 


Simplifying
x2 + 19x + 44 = 0

Reorder the terms:
44 + 19x + x2 = 0

Solving
44 + 19x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-44' to each side of the equation.
44 + 19x + -44 + x2 = 0 + -44

Reorder the terms:
44 + -44 + 19x + x2 = 0 + -44

Combine like terms: 44 + -44 = 0
0 + 19x + x2 = 0 + -44
19x + x2 = 0 + -44

Combine like terms: 0 + -44 = -44
19x + x2 = -44

The x term is 19x.  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.
19x + 90.25 + x2 = -44 + 90.25

Reorder the terms:
90.25 + 19x + x2 = -44 + 90.25

Combine like terms: -44 + 90.25 = 46.25
90.25 + 19x + x2 = 46.25

Factor a perfect square on the left side:
(x + 9.5)(x + 9.5) = 46.25

Calculate the square root of the right side: 6.800735254

Break this problem into two subproblems by setting 
(x + 9.5) equal to 6.800735254 and -6.800735254.


Subproblem 1
x + 9.5 = 6.800735254

Simplifying
x + 9.5 = 6.800735254

Reorder the terms:
9.5 + x = 6.800735254

Solving
9.5 + x = 6.800735254

Solving for variable 'x'.

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

Add '-9.5' to each side of the equation.
9.5 + -9.5 + x = 6.800735254 + -9.5

Combine like terms: 9.5 + -9.5 = 0.0
0.0 + x = 6.800735254 + -9.5
x = 6.800735254 + -9.5

Combine like terms: 6.800735254 + -9.5 = -2.699264746
x = -2.699264746

Simplifying
x = -2.699264746


Subproblem 2
x + 9.5 = -6.800735254

Simplifying
x + 9.5 = -6.800735254

Reorder the terms:
9.5 + x = -6.800735254

Solving
9.5 + x = -6.800735254

Solving for variable 'x'.

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

Add '-9.5' to each side of the equation.
9.5 + -9.5 + x = -6.800735254 + -9.5

Combine like terms: 9.5 + -9.5 = 0.0
0.0 + x = -6.800735254 + -9.5
x = -6.800735254 + -9.5

Combine like terms: -6.800735254 + -9.5 = -16.300735254
x = -16.300735254

Simplifying
x = -16.300735254


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.699264746, -16.300735254}

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