2x^2+24x+32=0

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Solution for 2x^2+24x+32=0 equation: 


Simplifying
2x2 + 24x + 32 = 0

Reorder the terms:
32 + 24x + 2x2 = 0

Solving
32 + 24x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(16 + 12x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(16 + 12x + x2)' equal to zero and attempt to solve:

Simplifying
16 + 12x + x2 = 0

Solving
16 + 12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + 12x + -16 + x2 = 0 + -16

Reorder the terms:
16 + -16 + 12x + x2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + 12x + x2 = 0 + -16
12x + x2 = 0 + -16

Combine like terms: 0 + -16 = -16
12x + x2 = -16

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 = -16 + 36

Reorder the terms:
36 + 12x + x2 = -16 + 36

Combine like terms: -16 + 36 = 20
36 + 12x + x2 = 20

Factor a perfect square on the left side:
(x + 6)(x + 6) = 20

Calculate the square root of the right side: 4.472135955

Break this problem into two subproblems by setting 
(x + 6) equal to 4.472135955 and -4.472135955.


Subproblem 1
x + 6 = 4.472135955

Simplifying
x + 6 = 4.472135955

Reorder the terms:
6 + x = 4.472135955

Solving
6 + x = 4.472135955

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 = 4.472135955 + -6

Combine like terms: 6 + -6 = 0
0 + x = 4.472135955 + -6
x = 4.472135955 + -6

Combine like terms: 4.472135955 + -6 = -1.527864045
x = -1.527864045

Simplifying
x = -1.527864045


Subproblem 2
x + 6 = -4.472135955

Simplifying
x + 6 = -4.472135955

Reorder the terms:
6 + x = -4.472135955

Solving
6 + x = -4.472135955

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 = -4.472135955 + -6

Combine like terms: 6 + -6 = 0
0 + x = -4.472135955 + -6
x = -4.472135955 + -6

Combine like terms: -4.472135955 + -6 = -10.472135955
x = -10.472135955

Simplifying
x = -10.472135955


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.527864045, -10.472135955}
Solution
x = {-1.527864045, -10.472135955}

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