-8x^2-19x-7=0

Solution for -8x^2-19x-7=0 equation:

Simplifying
-8x2 + -19x + -7 = 0

Reorder the terms:
-7 + -19x + -8x2 = 0

Solving
-7 + -19x + -8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(7 + 19x + 8x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(7 + 19x + 8x2)' equal to zero and attempt to solve:

Simplifying
7 + 19x + 8x2 = 0

Solving
7 + 19x + 8x2 = 0

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

Divide each side by '8'.
0.875 + 2.375x + x2 = 0

Move the constant term to the right:

Add '-0.875' to each side of the equation.
0.875 + 2.375x + -0.875 + x2 = 0 + -0.875

Reorder the terms:
0.875 + -0.875 + 2.375x + x2 = 0 + -0.875

Combine like terms: 0.875 + -0.875 = 0.000
0.000 + 2.375x + x2 = 0 + -0.875
2.375x + x2 = 0 + -0.875

Combine like terms: 0 + -0.875 = -0.875
2.375x + x2 = -0.875

The x term is 2.375x.  Take half its coefficient (1.1875).
Square it (1.41015625) and add it to both sides.

Add '1.41015625' to each side of the equation.
2.375x + 1.41015625 + x2 = -0.875 + 1.41015625

Reorder the terms:
1.41015625 + 2.375x + x2 = -0.875 + 1.41015625

Combine like terms: -0.875 + 1.41015625 = 0.53515625
1.41015625 + 2.375x + x2 = 0.53515625

Factor a perfect square on the left side:
(x + 1.1875)(x + 1.1875) = 0.53515625

Calculate the square root of the right side: 0.731543744

Break this problem into two subproblems by setting 
(x + 1.1875) equal to 0.731543744 and -0.731543744.

Subproblem 1
x + 1.1875 = 0.731543744

Simplifying
x + 1.1875 = 0.731543744

Reorder the terms:
1.1875 + x = 0.731543744

Solving
1.1875 + x = 0.731543744

Solving for variable 'x'.

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

Add '-1.1875' to each side of the equation.
1.1875 + -1.1875 + x = 0.731543744 + -1.1875

Combine like terms: 1.1875 + -1.1875 = 0.0000
0.0000 + x = 0.731543744 + -1.1875
x = 0.731543744 + -1.1875

Combine like terms: 0.731543744 + -1.1875 = -0.455956256
x = -0.455956256

Simplifying
x = -0.455956256

Subproblem 2
x + 1.1875 = -0.731543744

Simplifying
x + 1.1875 = -0.731543744

Reorder the terms:
1.1875 + x = -0.731543744

Solving
1.1875 + x = -0.731543744

Solving for variable 'x'.

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

Add '-1.1875' to each side of the equation.
1.1875 + -1.1875 + x = -0.731543744 + -1.1875

Combine like terms: 1.1875 + -1.1875 = 0.0000
0.0000 + x = -0.731543744 + -1.1875
x = -0.731543744 + -1.1875

Combine like terms: -0.731543744 + -1.1875 = -1.919043744
x = -1.919043744

Simplifying
x = -1.919043744

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.455956256, -1.919043744}
Solution
x = {-0.455956256, -1.919043744}