-8x^2-124x-352=-5x^2-79-184

Solution for -8x^2-124x-352=-5x^2-79-184 equation:

Simplifying
-8x2 + -124x + -352 = -5x2 + -79 + -184

Reorder the terms:
-352 + -124x + -8x2 = -5x2 + -79 + -184

Reorder the terms:
-352 + -124x + -8x2 = -79 + -184 + -5x2

Combine like terms: -79 + -184 = -263
-352 + -124x + -8x2 = -263 + -5x2

Solving
-352 + -124x + -8x2 = -263 + -5x2

Solving for variable 'x'.

Reorder the terms:
-352 + 263 + -124x + -8x2 + 5x2 = -263 + -5x2 + 263 + 5x2

Combine like terms: -352 + 263 = -89
-89 + -124x + -8x2 + 5x2 = -263 + -5x2 + 263 + 5x2

Combine like terms: -8x2 + 5x2 = -3x2
-89 + -124x + -3x2 = -263 + -5x2 + 263 + 5x2

Reorder the terms:
-89 + -124x + -3x2 = -263 + 263 + -5x2 + 5x2

Combine like terms: -263 + 263 = 0
-89 + -124x + -3x2 = 0 + -5x2 + 5x2
-89 + -124x + -3x2 = -5x2 + 5x2

Combine like terms: -5x2 + 5x2 = 0
-89 + -124x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(89 + 124x + 3x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(89 + 124x + 3x2)' equal to zero and attempt to solve:

Simplifying
89 + 124x + 3x2 = 0

Solving
89 + 124x + 3x2 = 0

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

Divide each side by '3'.
29.66666667 + 41.33333333x + x2 = 0

Move the constant term to the right:

Add '-29.66666667' to each side of the equation.
29.66666667 + 41.33333333x + -29.66666667 + x2 = 0 + -29.66666667

Reorder the terms:
29.66666667 + -29.66666667 + 41.33333333x + x2 = 0 + -29.66666667

Combine like terms: 29.66666667 + -29.66666667 = 0.00000000
0.00000000 + 41.33333333x + x2 = 0 + -29.66666667
41.33333333x + x2 = 0 + -29.66666667

Combine like terms: 0 + -29.66666667 = -29.66666667
41.33333333x + x2 = -29.66666667

The x term is 41.33333333x.  Take half its coefficient (20.66666667).
Square it (427.1111112) and add it to both sides.

Add '427.1111112' to each side of the equation.
41.33333333x + 427.1111112 + x2 = -29.66666667 + 427.1111112

Reorder the terms:
427.1111112 + 41.33333333x + x2 = -29.66666667 + 427.1111112

Combine like terms: -29.66666667 + 427.1111112 = 397.44444453
427.1111112 + 41.33333333x + x2 = 397.44444453

Factor a perfect square on the left side:
(x + 20.66666667)(x + 20.66666667) = 397.44444453

Calculate the square root of the right side: 19.936008741

Break this problem into two subproblems by setting 
(x + 20.66666667) equal to 19.936008741 and -19.936008741.

Subproblem 1
x + 20.66666667 = 19.936008741

Simplifying
x + 20.66666667 = 19.936008741

Reorder the terms:
20.66666667 + x = 19.936008741

Solving
20.66666667 + x = 19.936008741

Solving for variable 'x'.

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

Add '-20.66666667' to each side of the equation.
20.66666667 + -20.66666667 + x = 19.936008741 + -20.66666667

Combine like terms: 20.66666667 + -20.66666667 = 0.00000000
0.00000000 + x = 19.936008741 + -20.66666667
x = 19.936008741 + -20.66666667

Combine like terms: 19.936008741 + -20.66666667 = -0.730657929
x = -0.730657929

Simplifying
x = -0.730657929

Subproblem 2
x + 20.66666667 = -19.936008741

Simplifying
x + 20.66666667 = -19.936008741

Reorder the terms:
20.66666667 + x = -19.936008741

Solving
20.66666667 + x = -19.936008741

Solving for variable 'x'.

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

Add '-20.66666667' to each side of the equation.
20.66666667 + -20.66666667 + x = -19.936008741 + -20.66666667

Combine like terms: 20.66666667 + -20.66666667 = 0.00000000
0.00000000 + x = -19.936008741 + -20.66666667
x = -19.936008741 + -20.66666667

Combine like terms: -19.936008741 + -20.66666667 = -40.602675411
x = -40.602675411

Simplifying
x = -40.602675411

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.730657929, -40.602675411}
Solution
x = {-0.730657929, -40.602675411}