2x^2-32x-64=0

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Solution for 2x^2-32x-64=0 equation: 


Simplifying
2x2 + -32x + -64 = 0

Reorder the terms:
-64 + -32x + 2x2 = 0

Solving
-64 + -32x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-32 + -16x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-32 + -16x + x2)' equal to zero and attempt to solve:

Simplifying
-32 + -16x + x2 = 0

Solving
-32 + -16x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '32' to each side of the equation.
-32 + -16x + 32 + x2 = 0 + 32

Reorder the terms:
-32 + 32 + -16x + x2 = 0 + 32

Combine like terms: -32 + 32 = 0
0 + -16x + x2 = 0 + 32
-16x + x2 = 0 + 32

Combine like terms: 0 + 32 = 32
-16x + x2 = 32

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 = 32 + 64

Reorder the terms:
64 + -16x + x2 = 32 + 64

Combine like terms: 32 + 64 = 96
64 + -16x + x2 = 96

Factor a perfect square on the left side:
(x + -8)(x + -8) = 96

Calculate the square root of the right side: 9.797958971

Break this problem into two subproblems by setting 
(x + -8) equal to 9.797958971 and -9.797958971.


Subproblem 1
x + -8 = 9.797958971

Simplifying
x + -8 = 9.797958971

Reorder the terms:
-8 + x = 9.797958971

Solving
-8 + x = 9.797958971

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 = 9.797958971 + 8

Combine like terms: -8 + 8 = 0
0 + x = 9.797958971 + 8
x = 9.797958971 + 8

Combine like terms: 9.797958971 + 8 = 17.797958971
x = 17.797958971

Simplifying
x = 17.797958971


Subproblem 2
x + -8 = -9.797958971

Simplifying
x + -8 = -9.797958971

Reorder the terms:
-8 + x = -9.797958971

Solving
-8 + x = -9.797958971

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 = -9.797958971 + 8

Combine like terms: -8 + 8 = 0
0 + x = -9.797958971 + 8
x = -9.797958971 + 8

Combine like terms: -9.797958971 + 8 = -1.797958971
x = -1.797958971

Simplifying
x = -1.797958971


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.797958971, -1.797958971}
Solution
x = {17.797958971, -1.797958971}

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