2X^2-32X-128=0

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Solution for 2X^2-32X-128=0 equation: 


Simplifying
2X2 + -32X + -128 = 0

Reorder the terms:
-128 + -32X + 2X2 = 0

Solving
-128 + -32X + 2X2 = 0

Solving for variable 'X'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-64 + -16X + X2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-64 + -16X + X2)' equal to zero and attempt to solve:

Simplifying
-64 + -16X + X2 = 0

Solving
-64 + -16X + X2 = 0

Begin completing the square.

Move the constant term to the right:

Add '64' to each side of the equation.
-64 + -16X + 64 + X2 = 0 + 64

Reorder the terms:
-64 + 64 + -16X + X2 = 0 + 64

Combine like terms: -64 + 64 = 0
0 + -16X + X2 = 0 + 64
-16X + X2 = 0 + 64

Combine like terms: 0 + 64 = 64
-16X + X2 = 64

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 = 64 + 64

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

Combine like terms: 64 + 64 = 128
64 + -16X + X2 = 128

Factor a perfect square on the left side:
(X + -8)(X + -8) = 128

Calculate the square root of the right side: 11.313708499

Break this problem into two subproblems by setting 
(X + -8) equal to 11.313708499 and -11.313708499.


Subproblem 1
X + -8 = 11.313708499

Simplifying
X + -8 = 11.313708499

Reorder the terms:
-8 + X = 11.313708499

Solving
-8 + X = 11.313708499

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 = 11.313708499 + 8

Combine like terms: -8 + 8 = 0
0 + X = 11.313708499 + 8
X = 11.313708499 + 8

Combine like terms: 11.313708499 + 8 = 19.313708499
X = 19.313708499

Simplifying
X = 19.313708499


Subproblem 2
X + -8 = -11.313708499

Simplifying
X + -8 = -11.313708499

Reorder the terms:
-8 + X = -11.313708499

Solving
-8 + X = -11.313708499

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 = -11.313708499 + 8

Combine like terms: -8 + 8 = 0
0 + X = -11.313708499 + 8
X = -11.313708499 + 8

Combine like terms: -11.313708499 + 8 = -3.313708499
X = -3.313708499

Simplifying
X = -3.313708499


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {19.313708499, -3.313708499}
Solution
X = {19.313708499, -3.313708499}

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