x^2+19x+50=0

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Solution for x^2+19x+50=0 equation: 


Simplifying
x2 + 19x + 50 = 0

Reorder the terms:
50 + 19x + x2 = 0

Solving
50 + 19x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-50' to each side of the equation.
50 + 19x + -50 + x2 = 0 + -50

Reorder the terms:
50 + -50 + 19x + x2 = 0 + -50

Combine like terms: 50 + -50 = 0
0 + 19x + x2 = 0 + -50
19x + x2 = 0 + -50

Combine like terms: 0 + -50 = -50
19x + x2 = -50

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 = -50 + 90.25

Reorder the terms:
90.25 + 19x + x2 = -50 + 90.25

Combine like terms: -50 + 90.25 = 40.25
90.25 + 19x + x2 = 40.25

Factor a perfect square on the left side:
(x + 9.5)(x + 9.5) = 40.25

Calculate the square root of the right side: 6.34428877

Break this problem into two subproblems by setting 
(x + 9.5) equal to 6.34428877 and -6.34428877.


Subproblem 1
x + 9.5 = 6.34428877

Simplifying
x + 9.5 = 6.34428877

Reorder the terms:
9.5 + x = 6.34428877

Solving
9.5 + x = 6.34428877

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 = 6.34428877 + -9.5

Combine like terms: 9.5 + -9.5 = 0.0
0.0 + x = 6.34428877 + -9.5
x = 6.34428877 + -9.5

Combine like terms: 6.34428877 + -9.5 = -3.15571123
x = -3.15571123

Simplifying
x = -3.15571123


Subproblem 2
x + 9.5 = -6.34428877

Simplifying
x + 9.5 = -6.34428877

Reorder the terms:
9.5 + x = -6.34428877

Solving
9.5 + x = -6.34428877

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 = -6.34428877 + -9.5

Combine like terms: 9.5 + -9.5 = 0.0
0.0 + x = -6.34428877 + -9.5
x = -6.34428877 + -9.5

Combine like terms: -6.34428877 + -9.5 = -15.84428877
x = -15.84428877

Simplifying
x = -15.84428877


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-3.15571123, -15.84428877}

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