2x^2+14x=-8x-32

Solution for 2x^2+14x=-8x-32 equation:

Simplifying
2x2 + 14x = -8x + -32

Reorder the terms:
14x + 2x2 = -8x + -32

Reorder the terms:
14x + 2x2 = -32 + -8x

Solving
14x + 2x2 = -32 + -8x

Solving for variable 'x'.

Reorder the terms:
32 + 14x + 8x + 2x2 = -32 + -8x + 32 + 8x

Combine like terms: 14x + 8x = 22x
32 + 22x + 2x2 = -32 + -8x + 32 + 8x

Reorder the terms:
32 + 22x + 2x2 = -32 + 32 + -8x + 8x

Combine like terms: -32 + 32 = 0
32 + 22x + 2x2 = 0 + -8x + 8x
32 + 22x + 2x2 = -8x + 8x

Combine like terms: -8x + 8x = 0
32 + 22x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(16 + 11x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(16 + 11x + x2)' equal to zero and attempt to solve:

Simplifying
16 + 11x + x2 = 0

Solving
16 + 11x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + 11x + -16 + x2 = 0 + -16

Reorder the terms:
16 + -16 + 11x + x2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + 11x + x2 = 0 + -16
11x + x2 = 0 + -16

Combine like terms: 0 + -16 = -16
11x + x2 = -16

The x term is 11x.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11x + 30.25 + x2 = -16 + 30.25

Reorder the terms:
30.25 + 11x + x2 = -16 + 30.25

Combine like terms: -16 + 30.25 = 14.25
30.25 + 11x + x2 = 14.25

Factor a perfect square on the left side:
(x + 5.5)(x + 5.5) = 14.25

Calculate the square root of the right side: 3.774917218

Break this problem into two subproblems by setting 
(x + 5.5) equal to 3.774917218 and -3.774917218.

Subproblem 1
x + 5.5 = 3.774917218

Simplifying
x + 5.5 = 3.774917218

Reorder the terms:
5.5 + x = 3.774917218

Solving
5.5 + x = 3.774917218

Solving for variable 'x'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + x = 3.774917218 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = 3.774917218 + -5.5
x = 3.774917218 + -5.5

Combine like terms: 3.774917218 + -5.5 = -1.725082782
x = -1.725082782

Simplifying
x = -1.725082782

Subproblem 2
x + 5.5 = -3.774917218

Simplifying
x + 5.5 = -3.774917218

Reorder the terms:
5.5 + x = -3.774917218

Solving
5.5 + x = -3.774917218

Solving for variable 'x'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + x = -3.774917218 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = -3.774917218 + -5.5
x = -3.774917218 + -5.5

Combine like terms: -3.774917218 + -5.5 = -9.274917218
x = -9.274917218

Simplifying
x = -9.274917218

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.725082782, -9.274917218}
Solution
x = {-1.725082782, -9.274917218}