-8x^2-28x-19=0

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Solution for -8x^2-28x-19=0 equation: 


Simplifying
-8x2 + -28x + -19 = 0

Reorder the terms:
-19 + -28x + -8x2 = 0

Solving
-19 + -28x + -8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(19 + 28x + 8x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(19 + 28x + 8x2)' equal to zero and attempt to solve:

Simplifying
19 + 28x + 8x2 = 0

Solving
19 + 28x + 8x2 = 0

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

Divide each side by '8'.
2.375 + 3.5x + x2 = 0

Move the constant term to the right:

Add '-2.375' to each side of the equation.
2.375 + 3.5x + -2.375 + x2 = 0 + -2.375

Reorder the terms:
2.375 + -2.375 + 3.5x + x2 = 0 + -2.375

Combine like terms: 2.375 + -2.375 = 0.000
0.000 + 3.5x + x2 = 0 + -2.375
3.5x + x2 = 0 + -2.375

Combine like terms: 0 + -2.375 = -2.375
3.5x + x2 = -2.375

The x term is 3.5x.  Take half its coefficient (1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
3.5x + 3.0625 + x2 = -2.375 + 3.0625

Reorder the terms:
3.0625 + 3.5x + x2 = -2.375 + 3.0625

Combine like terms: -2.375 + 3.0625 = 0.6875
3.0625 + 3.5x + x2 = 0.6875

Factor a perfect square on the left side:
(x + 1.75)(x + 1.75) = 0.6875

Calculate the square root of the right side: 0.829156198

Break this problem into two subproblems by setting 
(x + 1.75) equal to 0.829156198 and -0.829156198.


Subproblem 1
x + 1.75 = 0.829156198

Simplifying
x + 1.75 = 0.829156198

Reorder the terms:
1.75 + x = 0.829156198

Solving
1.75 + x = 0.829156198

Solving for variable 'x'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + x = 0.829156198 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + x = 0.829156198 + -1.75
x = 0.829156198 + -1.75

Combine like terms: 0.829156198 + -1.75 = -0.920843802
x = -0.920843802

Simplifying
x = -0.920843802


Subproblem 2
x + 1.75 = -0.829156198

Simplifying
x + 1.75 = -0.829156198

Reorder the terms:
1.75 + x = -0.829156198

Solving
1.75 + x = -0.829156198

Solving for variable 'x'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + x = -0.829156198 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + x = -0.829156198 + -1.75
x = -0.829156198 + -1.75

Combine like terms: -0.829156198 + -1.75 = -2.579156198
x = -2.579156198

Simplifying
x = -2.579156198


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.920843802, -2.579156198}
Solution
x = {-0.920843802, -2.579156198}

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