5x^2+19x+8=0

Solution for 5x^2+19x+8=0 equation:

Simplifying
5x2 + 19x + 8 = 0

Reorder the terms:
8 + 19x + 5x2 = 0

Solving
8 + 19x + 5x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
1.6 + 3.8x + x2 = 0

Move the constant term to the right:

Add '-1.6' to each side of the equation.
1.6 + 3.8x + -1.6 + x2 = 0 + -1.6

Reorder the terms:
1.6 + -1.6 + 3.8x + x2 = 0 + -1.6

Combine like terms: 1.6 + -1.6 = 0.0
0.0 + 3.8x + x2 = 0 + -1.6
3.8x + x2 = 0 + -1.6

Combine like terms: 0 + -1.6 = -1.6
3.8x + x2 = -1.6

The x term is 3.8x.  Take half its coefficient (1.9).
Square it (3.61) and add it to both sides.

Add '3.61' to each side of the equation.
3.8x + 3.61 + x2 = -1.6 + 3.61

Reorder the terms:
3.61 + 3.8x + x2 = -1.6 + 3.61

Combine like terms: -1.6 + 3.61 = 2.01
3.61 + 3.8x + x2 = 2.01

Factor a perfect square on the left side:
(x + 1.9)(x + 1.9) = 2.01

Calculate the square root of the right side: 1.417744688

Break this problem into two subproblems by setting 
(x + 1.9) equal to 1.417744688 and -1.417744688.

Subproblem 1
x + 1.9 = 1.417744688

Simplifying
x + 1.9 = 1.417744688

Reorder the terms:
1.9 + x = 1.417744688

Solving
1.9 + x = 1.417744688

Solving for variable 'x'.

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

Add '-1.9' to each side of the equation.
1.9 + -1.9 + x = 1.417744688 + -1.9

Combine like terms: 1.9 + -1.9 = 0.0
0.0 + x = 1.417744688 + -1.9
x = 1.417744688 + -1.9

Combine like terms: 1.417744688 + -1.9 = -0.482255312
x = -0.482255312

Simplifying
x = -0.482255312

Subproblem 2
x + 1.9 = -1.417744688

Simplifying
x + 1.9 = -1.417744688

Reorder the terms:
1.9 + x = -1.417744688

Solving
1.9 + x = -1.417744688

Solving for variable 'x'.

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

Add '-1.9' to each side of the equation.
1.9 + -1.9 + x = -1.417744688 + -1.9

Combine like terms: 1.9 + -1.9 = 0.0
0.0 + x = -1.417744688 + -1.9
x = -1.417744688 + -1.9

Combine like terms: -1.417744688 + -1.9 = -3.317744688
x = -3.317744688

Simplifying
x = -3.317744688

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.482255312, -3.317744688}