x^2+19x+38=0

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Solution for x^2+19x+38=0 equation: 


Simplifying
x2 + 19x + 38 = 0

Reorder the terms:
38 + 19x + x2 = 0

Solving
38 + 19x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-38' to each side of the equation.
38 + 19x + -38 + x2 = 0 + -38

Reorder the terms:
38 + -38 + 19x + x2 = 0 + -38

Combine like terms: 38 + -38 = 0
0 + 19x + x2 = 0 + -38
19x + x2 = 0 + -38

Combine like terms: 0 + -38 = -38
19x + x2 = -38

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 = -38 + 90.25

Reorder the terms:
90.25 + 19x + x2 = -38 + 90.25

Combine like terms: -38 + 90.25 = 52.25
90.25 + 19x + x2 = 52.25

Factor a perfect square on the left side:
(x + 9.5)(x + 9.5) = 52.25

Calculate the square root of the right side: 7.228416147

Break this problem into two subproblems by setting 
(x + 9.5) equal to 7.228416147 and -7.228416147.


Subproblem 1
x + 9.5 = 7.228416147

Simplifying
x + 9.5 = 7.228416147

Reorder the terms:
9.5 + x = 7.228416147

Solving
9.5 + x = 7.228416147

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 = 7.228416147 + -9.5

Combine like terms: 9.5 + -9.5 = 0.0
0.0 + x = 7.228416147 + -9.5
x = 7.228416147 + -9.5

Combine like terms: 7.228416147 + -9.5 = -2.271583853
x = -2.271583853

Simplifying
x = -2.271583853


Subproblem 2
x + 9.5 = -7.228416147

Simplifying
x + 9.5 = -7.228416147

Reorder the terms:
9.5 + x = -7.228416147

Solving
9.5 + x = -7.228416147

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 = -7.228416147 + -9.5

Combine like terms: 9.5 + -9.5 = 0.0
0.0 + x = -7.228416147 + -9.5
x = -7.228416147 + -9.5

Combine like terms: -7.228416147 + -9.5 = -16.728416147
x = -16.728416147

Simplifying
x = -16.728416147


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.271583853, -16.728416147}

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