2x^2+32x-3888=0

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Solution for 2x^2+32x-3888=0 equation: 


Simplifying
2x2 + 32x + -3888 = 0

Reorder the terms:
-3888 + 32x + 2x2 = 0

Solving
-3888 + 32x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1944 + 16x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-1944 + 16x + x2)' equal to zero and attempt to solve:

Simplifying
-1944 + 16x + x2 = 0

Solving
-1944 + 16x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1944' to each side of the equation.
-1944 + 16x + 1944 + x2 = 0 + 1944

Reorder the terms:
-1944 + 1944 + 16x + x2 = 0 + 1944

Combine like terms: -1944 + 1944 = 0
0 + 16x + x2 = 0 + 1944
16x + x2 = 0 + 1944

Combine like terms: 0 + 1944 = 1944
16x + x2 = 1944

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 = 1944 + 64

Reorder the terms:
64 + 16x + x2 = 1944 + 64

Combine like terms: 1944 + 64 = 2008
64 + 16x + x2 = 2008

Factor a perfect square on the left side:
(x + 8)(x + 8) = 2008

Calculate the square root of the right side: 44.810713005

Break this problem into two subproblems by setting 
(x + 8) equal to 44.810713005 and -44.810713005.


Subproblem 1
x + 8 = 44.810713005

Simplifying
x + 8 = 44.810713005

Reorder the terms:
8 + x = 44.810713005

Solving
8 + x = 44.810713005

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 = 44.810713005 + -8

Combine like terms: 8 + -8 = 0
0 + x = 44.810713005 + -8
x = 44.810713005 + -8

Combine like terms: 44.810713005 + -8 = 36.810713005
x = 36.810713005

Simplifying
x = 36.810713005


Subproblem 2
x + 8 = -44.810713005

Simplifying
x + 8 = -44.810713005

Reorder the terms:
8 + x = -44.810713005

Solving
8 + x = -44.810713005

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 = -44.810713005 + -8

Combine like terms: 8 + -8 = 0
0 + x = -44.810713005 + -8
x = -44.810713005 + -8

Combine like terms: -44.810713005 + -8 = -52.810713005
x = -52.810713005

Simplifying
x = -52.810713005


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {36.810713005, -52.810713005}
Solution
x = {36.810713005, -52.810713005}

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