3x^2-32x-64=0

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Solution for 3x^2-32x-64=0 equation: 


Simplifying
3x2 + -32x + -64 = 0

Reorder the terms:
-64 + -32x + 3x2 = 0

Solving
-64 + -32x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-21.33333333 + -10.66666667x + x2 = 0

Move the constant term to the right:

Add '21.33333333' to each side of the equation.
-21.33333333 + -10.66666667x + 21.33333333 + x2 = 0 + 21.33333333

Reorder the terms:
-21.33333333 + 21.33333333 + -10.66666667x + x2 = 0 + 21.33333333

Combine like terms: -21.33333333 + 21.33333333 = 0.00000000
0.00000000 + -10.66666667x + x2 = 0 + 21.33333333
-10.66666667x + x2 = 0 + 21.33333333

Combine like terms: 0 + 21.33333333 = 21.33333333
-10.66666667x + x2 = 21.33333333

The x term is -10.66666667x.  Take half its coefficient (-5.333333335).
Square it (28.44444446) and add it to both sides.

Add '28.44444446' to each side of the equation.
-10.66666667x + 28.44444446 + x2 = 21.33333333 + 28.44444446

Reorder the terms:
28.44444446 + -10.66666667x + x2 = 21.33333333 + 28.44444446

Combine like terms: 21.33333333 + 28.44444446 = 49.77777779
28.44444446 + -10.66666667x + x2 = 49.77777779

Factor a perfect square on the left side:
(x + -5.333333335)(x + -5.333333335) = 49.77777779

Calculate the square root of the right side: 7.05533683

Break this problem into two subproblems by setting 
(x + -5.333333335) equal to 7.05533683 and -7.05533683.


Subproblem 1
x + -5.333333335 = 7.05533683

Simplifying
x + -5.333333335 = 7.05533683

Reorder the terms:
-5.333333335 + x = 7.05533683

Solving
-5.333333335 + x = 7.05533683

Solving for variable 'x'.

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

Add '5.333333335' to each side of the equation.
-5.333333335 + 5.333333335 + x = 7.05533683 + 5.333333335

Combine like terms: -5.333333335 + 5.333333335 = 0.000000000
0.000000000 + x = 7.05533683 + 5.333333335
x = 7.05533683 + 5.333333335

Combine like terms: 7.05533683 + 5.333333335 = 12.388670165
x = 12.388670165

Simplifying
x = 12.388670165


Subproblem 2
x + -5.333333335 = -7.05533683

Simplifying
x + -5.333333335 = -7.05533683

Reorder the terms:
-5.333333335 + x = -7.05533683

Solving
-5.333333335 + x = -7.05533683

Solving for variable 'x'.

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

Add '5.333333335' to each side of the equation.
-5.333333335 + 5.333333335 + x = -7.05533683 + 5.333333335

Combine like terms: -5.333333335 + 5.333333335 = 0.000000000
0.000000000 + x = -7.05533683 + 5.333333335
x = -7.05533683 + 5.333333335

Combine like terms: -7.05533683 + 5.333333335 = -1.722003495
x = -1.722003495

Simplifying
x = -1.722003495


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.388670165, -1.722003495}

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