8x^2-92x-1320=0

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Solution for 8x^2-92x-1320=0 equation: 


Simplifying
8x2 + -92x + -1320 = 0

Reorder the terms:
-1320 + -92x + 8x2 = 0

Solving
-1320 + -92x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-330 + -23x + 2x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-330 + -23x + 2x2)' equal to zero and attempt to solve:

Simplifying
-330 + -23x + 2x2 = 0

Solving
-330 + -23x + 2x2 = 0

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

Divide each side by '2'.
-165 + -11.5x + x2 = 0

Move the constant term to the right:

Add '165' to each side of the equation.
-165 + -11.5x + 165 + x2 = 0 + 165

Reorder the terms:
-165 + 165 + -11.5x + x2 = 0 + 165

Combine like terms: -165 + 165 = 0
0 + -11.5x + x2 = 0 + 165
-11.5x + x2 = 0 + 165

Combine like terms: 0 + 165 = 165
-11.5x + x2 = 165

The x term is -11.5x.  Take half its coefficient (-5.75).
Square it (33.0625) and add it to both sides.

Add '33.0625' to each side of the equation.
-11.5x + 33.0625 + x2 = 165 + 33.0625

Reorder the terms:
33.0625 + -11.5x + x2 = 165 + 33.0625

Combine like terms: 165 + 33.0625 = 198.0625
33.0625 + -11.5x + x2 = 198.0625

Factor a perfect square on the left side:
(x + -5.75)(x + -5.75) = 198.0625

Calculate the square root of the right side: 14.073467945

Break this problem into two subproblems by setting 
(x + -5.75) equal to 14.073467945 and -14.073467945.


Subproblem 1
x + -5.75 = 14.073467945

Simplifying
x + -5.75 = 14.073467945

Reorder the terms:
-5.75 + x = 14.073467945

Solving
-5.75 + x = 14.073467945

Solving for variable 'x'.

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

Add '5.75' to each side of the equation.
-5.75 + 5.75 + x = 14.073467945 + 5.75

Combine like terms: -5.75 + 5.75 = 0.00
0.00 + x = 14.073467945 + 5.75
x = 14.073467945 + 5.75

Combine like terms: 14.073467945 + 5.75 = 19.823467945
x = 19.823467945

Simplifying
x = 19.823467945


Subproblem 2
x + -5.75 = -14.073467945

Simplifying
x + -5.75 = -14.073467945

Reorder the terms:
-5.75 + x = -14.073467945

Solving
-5.75 + x = -14.073467945

Solving for variable 'x'.

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

Add '5.75' to each side of the equation.
-5.75 + 5.75 + x = -14.073467945 + 5.75

Combine like terms: -5.75 + 5.75 = 0.00
0.00 + x = -14.073467945 + 5.75
x = -14.073467945 + 5.75

Combine like terms: -14.073467945 + 5.75 = -8.323467945
x = -8.323467945

Simplifying
x = -8.323467945


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {19.823467945, -8.323467945}
Solution
x = {19.823467945, -8.323467945}

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