2x^2+32x+24=0

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


Simplifying
2x2 + 32x + 24 = 0

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

Solving
24 + 32x + 2x2 = 0

Solving for variable 'x'.

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

Ignore the factor 2.

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

Simplifying
12 + 16x + x2 = 0

Solving
12 + 16x + x2 = 0

Begin completing the square.

Move the constant term to the right:

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

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

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

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

The x term is 16x.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16x + 64 + x2 = -12 + 64

Reorder the terms:
64 + 16x + x2 = -12 + 64

Combine like terms: -12 + 64 = 52
64 + 16x + x2 = 52

Factor a perfect square on the left side:
(x + 8)(x + 8) = 52

Calculate the square root of the right side: 7.211102551

Break this problem into two subproblems by setting 
(x + 8) equal to 7.211102551 and -7.211102551.


Subproblem 1
x + 8 = 7.211102551

Simplifying
x + 8 = 7.211102551

Reorder the terms:
8 + x = 7.211102551

Solving
8 + x = 7.211102551

Solving for variable 'x'.

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

Add '-8' to each side of the equation.
8 + -8 + x = 7.211102551 + -8

Combine like terms: 8 + -8 = 0
0 + x = 7.211102551 + -8
x = 7.211102551 + -8

Combine like terms: 7.211102551 + -8 = -0.788897449
x = -0.788897449

Simplifying
x = -0.788897449


Subproblem 2
x + 8 = -7.211102551

Simplifying
x + 8 = -7.211102551

Reorder the terms:
8 + x = -7.211102551

Solving
8 + x = -7.211102551

Solving for variable 'x'.

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

Add '-8' to each side of the equation.
8 + -8 + x = -7.211102551 + -8

Combine like terms: 8 + -8 = 0
0 + x = -7.211102551 + -8
x = -7.211102551 + -8

Combine like terms: -7.211102551 + -8 = -15.211102551
x = -15.211102551

Simplifying
x = -15.211102551


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.788897449, -15.211102551}
Solution
x = {-0.788897449, -15.211102551}

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