6x^2-3x-64=0

Solution for 6x^2-3x-64=0 equation:

Simplifying
6x2 + -3x + -64 = 0

Reorder the terms:
-64 + -3x + 6x2 = 0

Solving
-64 + -3x + 6x2 = 0

Solving for variable 'x'.

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

Divide each side by '6'.
-10.66666667 + -0.5x + x2 = 0

Move the constant term to the right:

Add '10.66666667' to each side of the equation.
-10.66666667 + -0.5x + 10.66666667 + x2 = 0 + 10.66666667

Reorder the terms:
-10.66666667 + 10.66666667 + -0.5x + x2 = 0 + 10.66666667

Combine like terms: -10.66666667 + 10.66666667 = 0.00000000
0.00000000 + -0.5x + x2 = 0 + 10.66666667
-0.5x + x2 = 0 + 10.66666667

Combine like terms: 0 + 10.66666667 = 10.66666667
-0.5x + x2 = 10.66666667

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 = 10.66666667 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = 10.66666667 + 0.0625

Combine like terms: 10.66666667 + 0.0625 = 10.72916667
0.0625 + -0.5x + x2 = 10.72916667

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = 10.72916667

Calculate the square root of the right side: 3.275540668

Break this problem into two subproblems by setting 
(x + -0.25) equal to 3.275540668 and -3.275540668.

Subproblem 1
x + -0.25 = 3.275540668

Simplifying
x + -0.25 = 3.275540668

Reorder the terms:
-0.25 + x = 3.275540668

Solving
-0.25 + x = 3.275540668

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 = 3.275540668 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = 3.275540668 + 0.25
x = 3.275540668 + 0.25

Combine like terms: 3.275540668 + 0.25 = 3.525540668
x = 3.525540668

Simplifying
x = 3.525540668

Subproblem 2
x + -0.25 = -3.275540668

Simplifying
x + -0.25 = -3.275540668

Reorder the terms:
-0.25 + x = -3.275540668

Solving
-0.25 + x = -3.275540668

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 = -3.275540668 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = -3.275540668 + 0.25
x = -3.275540668 + 0.25

Combine like terms: -3.275540668 + 0.25 = -3.025540668
x = -3.025540668

Simplifying
x = -3.025540668

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.525540668, -3.025540668}