64x^2-32x-6=0

Solution for 64x^2-32x-6=0 equation:

Simplifying
64x2 + -32x + -6 = 0

Reorder the terms:
-6 + -32x + 64x2 = 0

Solving
-6 + -32x + 64x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -16x + 32x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + -16x + 32x2)' equal to zero and attempt to solve:

Simplifying
-3 + -16x + 32x2 = 0

Solving
-3 + -16x + 32x2 = 0

Begin completing the square.  Divide all terms by
32 the coefficient of the squared term: 

Divide each side by '32'.
-0.09375 + -0.5x + x2 = 0

Move the constant term to the right:

Add '0.09375' to each side of the equation.
-0.09375 + -0.5x + 0.09375 + x2 = 0 + 0.09375

Reorder the terms:
-0.09375 + 0.09375 + -0.5x + x2 = 0 + 0.09375

Combine like terms: -0.09375 + 0.09375 = 0.00000
0.00000 + -0.5x + x2 = 0 + 0.09375
-0.5x + x2 = 0 + 0.09375

Combine like terms: 0 + 0.09375 = 0.09375
-0.5x + x2 = 0.09375

The x term is -0.5x.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x + 0.0625 + x2 = 0.09375 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = 0.09375 + 0.0625

Combine like terms: 0.09375 + 0.0625 = 0.15625
0.0625 + -0.5x + x2 = 0.15625

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = 0.15625

Calculate the square root of the right side: 0.395284708

Break this problem into two subproblems by setting 
(x + -0.25) equal to 0.395284708 and -0.395284708.

Subproblem 1
x + -0.25 = 0.395284708

Simplifying
x + -0.25 = 0.395284708

Reorder the terms:
-0.25 + x = 0.395284708

Solving
-0.25 + x = 0.395284708

Solving for variable 'x'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + x = 0.395284708 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = 0.395284708 + 0.25
x = 0.395284708 + 0.25

Combine like terms: 0.395284708 + 0.25 = 0.645284708
x = 0.645284708

Simplifying
x = 0.645284708

Subproblem 2
x + -0.25 = -0.395284708

Simplifying
x + -0.25 = -0.395284708

Reorder the terms:
-0.25 + x = -0.395284708

Solving
-0.25 + x = -0.395284708

Solving for variable 'x'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + x = -0.395284708 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = -0.395284708 + 0.25
x = -0.395284708 + 0.25

Combine like terms: -0.395284708 + 0.25 = -0.145284708
x = -0.145284708

Simplifying
x = -0.145284708

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.645284708, -0.145284708}
Solution
x = {0.645284708, -0.145284708}