2x^2+24x=-8

Solution for 2x^2+24x=-8 equation:

Simplifying
2x2 + 24x = -8

Reorder the terms:
24x + 2x2 = -8

Solving
24x + 2x2 = -8

Solving for variable 'x'.

Reorder the terms:
8 + 24x + 2x2 = -8 + 8

Combine like terms: -8 + 8 = 0
8 + 24x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + 12x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(4 + 12x + x2)' equal to zero and attempt to solve:

Simplifying
4 + 12x + x2 = 0

Solving
4 + 12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + 12x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + 12x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 12x + x2 = 0 + -4
12x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
12x + x2 = -4

The x term is 12x.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12x + 36 + x2 = -4 + 36

Reorder the terms:
36 + 12x + x2 = -4 + 36

Combine like terms: -4 + 36 = 32
36 + 12x + x2 = 32

Factor a perfect square on the left side:
(x + 6)(x + 6) = 32

Calculate the square root of the right side: 5.656854249

Break this problem into two subproblems by setting 
(x + 6) equal to 5.656854249 and -5.656854249.

Subproblem 1
x + 6 = 5.656854249

Simplifying
x + 6 = 5.656854249

Reorder the terms:
6 + x = 5.656854249

Solving
6 + x = 5.656854249

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = 5.656854249 + -6

Combine like terms: 6 + -6 = 0
0 + x = 5.656854249 + -6
x = 5.656854249 + -6

Combine like terms: 5.656854249 + -6 = -0.343145751
x = -0.343145751

Simplifying
x = -0.343145751

Subproblem 2
x + 6 = -5.656854249

Simplifying
x + 6 = -5.656854249

Reorder the terms:
6 + x = -5.656854249

Solving
6 + x = -5.656854249

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = -5.656854249 + -6

Combine like terms: 6 + -6 = 0
0 + x = -5.656854249 + -6
x = -5.656854249 + -6

Combine like terms: -5.656854249 + -6 = -11.656854249
x = -11.656854249

Simplifying
x = -11.656854249

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.343145751, -11.656854249}
Solution
x = {-0.343145751, -11.656854249}