2X^2+32X+32=0

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Solution for 2X^2+32X+32=0 equation: 


Simplifying
2X2 + 32X + 32 = 0

Reorder the terms:
32 + 32X + 2X2 = 0

Solving
32 + 32X + 2X2 = 0

Solving for variable 'X'.

Factor out the Greatest Common Factor (GCF), '2'.
2(16 + 16X + X2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(16 + 16X + X2)' equal to zero and attempt to solve:

Simplifying
16 + 16X + X2 = 0

Solving
16 + 16X + X2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + 16X + -16 + X2 = 0 + -16

Reorder the terms:
16 + -16 + 16X + X2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + 16X + X2 = 0 + -16
16X + X2 = 0 + -16

Combine like terms: 0 + -16 = -16
16X + X2 = -16

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 = -16 + 64

Reorder the terms:
64 + 16X + X2 = -16 + 64

Combine like terms: -16 + 64 = 48
64 + 16X + X2 = 48

Factor a perfect square on the left side:
(X + 8)(X + 8) = 48

Calculate the square root of the right side: 6.92820323

Break this problem into two subproblems by setting 
(X + 8) equal to 6.92820323 and -6.92820323.


Subproblem 1
X + 8 = 6.92820323

Simplifying
X + 8 = 6.92820323

Reorder the terms:
8 + X = 6.92820323

Solving
8 + X = 6.92820323

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 = 6.92820323 + -8

Combine like terms: 8 + -8 = 0
0 + X = 6.92820323 + -8
X = 6.92820323 + -8

Combine like terms: 6.92820323 + -8 = -1.07179677
X = -1.07179677

Simplifying
X = -1.07179677


Subproblem 2
X + 8 = -6.92820323

Simplifying
X + 8 = -6.92820323

Reorder the terms:
8 + X = -6.92820323

Solving
8 + X = -6.92820323

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 = -6.92820323 + -8

Combine like terms: 8 + -8 = 0
0 + X = -6.92820323 + -8
X = -6.92820323 + -8

Combine like terms: -6.92820323 + -8 = -14.92820323
X = -14.92820323

Simplifying
X = -14.92820323


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {-1.07179677, -14.92820323}
Solution
X = {-1.07179677, -14.92820323}

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