8x^2-32x-64=0

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Solution for 8x^2-32x-64=0 equation: 


Simplifying
8x2 + -32x + -64 = 0

Reorder the terms:
-64 + -32x + 8x2 = 0

Solving
-64 + -32x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8'.
8(-8 + -4x + x2) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(-8 + -4x + x2)' equal to zero and attempt to solve:

Simplifying
-8 + -4x + x2 = 0

Solving
-8 + -4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + -4x + 8 + x2 = 0 + 8

Reorder the terms:
-8 + 8 + -4x + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -4x + x2 = 0 + 8
-4x + x2 = 0 + 8

Combine like terms: 0 + 8 = 8
-4x + x2 = 8

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 8 + 4

Reorder the terms:
4 + -4x + x2 = 8 + 4

Combine like terms: 8 + 4 = 12
4 + -4x + x2 = 12

Factor a perfect square on the left side:
(x + -2)(x + -2) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(x + -2) equal to 3.464101615 and -3.464101615.


Subproblem 1
x + -2 = 3.464101615

Simplifying
x + -2 = 3.464101615

Reorder the terms:
-2 + x = 3.464101615

Solving
-2 + x = 3.464101615

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 3.464101615 + 2

Combine like terms: -2 + 2 = 0
0 + x = 3.464101615 + 2
x = 3.464101615 + 2

Combine like terms: 3.464101615 + 2 = 5.464101615
x = 5.464101615

Simplifying
x = 5.464101615


Subproblem 2
x + -2 = -3.464101615

Simplifying
x + -2 = -3.464101615

Reorder the terms:
-2 + x = -3.464101615

Solving
-2 + x = -3.464101615

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -3.464101615 + 2

Combine like terms: -2 + 2 = 0
0 + x = -3.464101615 + 2
x = -3.464101615 + 2

Combine like terms: -3.464101615 + 2 = -1.464101615
x = -1.464101615

Simplifying
x = -1.464101615


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.464101615, -1.464101615}
Solution
x = {5.464101615, -1.464101615}

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