2x^2+24x+16=0

Solution for 2x^2+24x+16=0 equation:

Simplifying
2x2 + 24x + 16 = 0

Reorder the terms:
16 + 24x + 2x2 = 0

Solving
16 + 24x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(8 + 12x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(8 + 12x + x2)' equal to zero and attempt to solve:

Simplifying
8 + 12x + x2 = 0

Solving
8 + 12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + 12x + -8 + x2 = 0 + -8

Reorder the terms:
8 + -8 + 12x + x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 12x + x2 = 0 + -8
12x + x2 = 0 + -8

Combine like terms: 0 + -8 = -8
12x + x2 = -8

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 = -8 + 36

Reorder the terms:
36 + 12x + x2 = -8 + 36

Combine like terms: -8 + 36 = 28
36 + 12x + x2 = 28

Factor a perfect square on the left side:
(x + 6)(x + 6) = 28

Calculate the square root of the right side: 5.291502622

Break this problem into two subproblems by setting 
(x + 6) equal to 5.291502622 and -5.291502622.

Subproblem 1
x + 6 = 5.291502622

Simplifying
x + 6 = 5.291502622

Reorder the terms:
6 + x = 5.291502622

Solving
6 + x = 5.291502622

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 = 5.291502622 + -6

Combine like terms: 6 + -6 = 0
0 + x = 5.291502622 + -6
x = 5.291502622 + -6

Combine like terms: 5.291502622 + -6 = -0.708497378
x = -0.708497378

Simplifying
x = -0.708497378

Subproblem 2
x + 6 = -5.291502622

Simplifying
x + 6 = -5.291502622

Reorder the terms:
6 + x = -5.291502622

Solving
6 + x = -5.291502622

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 = -5.291502622 + -6

Combine like terms: 6 + -6 = 0
0 + x = -5.291502622 + -6
x = -5.291502622 + -6

Combine like terms: -5.291502622 + -6 = -11.291502622
x = -11.291502622

Simplifying
x = -11.291502622

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.708497378, -11.291502622}
Solution
x = {-0.708497378, -11.291502622}