4x^2-8x-64=0

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Solution for 4x^2-8x-64=0 equation: 


Simplifying
4x2 + -8x + -64 = 0

Reorder the terms:
-64 + -8x + 4x2 = 0

Solving
-64 + -8x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-16 + -2x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-16 + -2x + x2)' equal to zero and attempt to solve:

Simplifying
-16 + -2x + x2 = 0

Solving
-16 + -2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + -2x + 16 + x2 = 0 + 16

Reorder the terms:
-16 + 16 + -2x + x2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -2x + x2 = 0 + 16
-2x + x2 = 0 + 16

Combine like terms: 0 + 16 = 16
-2x + x2 = 16

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 16 + 1

Reorder the terms:
1 + -2x + x2 = 16 + 1

Combine like terms: 16 + 1 = 17
1 + -2x + x2 = 17

Factor a perfect square on the left side:
(x + -1)(x + -1) = 17

Calculate the square root of the right side: 4.123105626

Break this problem into two subproblems by setting 
(x + -1) equal to 4.123105626 and -4.123105626.


Subproblem 1
x + -1 = 4.123105626

Simplifying
x + -1 = 4.123105626

Reorder the terms:
-1 + x = 4.123105626

Solving
-1 + x = 4.123105626

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 4.123105626 + 1

Combine like terms: -1 + 1 = 0
0 + x = 4.123105626 + 1
x = 4.123105626 + 1

Combine like terms: 4.123105626 + 1 = 5.123105626
x = 5.123105626

Simplifying
x = 5.123105626


Subproblem 2
x + -1 = -4.123105626

Simplifying
x + -1 = -4.123105626

Reorder the terms:
-1 + x = -4.123105626

Solving
-1 + x = -4.123105626

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -4.123105626 + 1

Combine like terms: -1 + 1 = 0
0 + x = -4.123105626 + 1
x = -4.123105626 + 1

Combine like terms: -4.123105626 + 1 = -3.123105626
x = -3.123105626

Simplifying
x = -3.123105626


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.123105626, -3.123105626}
Solution
x = {5.123105626, -3.123105626}

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