3x^2-24x-64=0

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Solution for 3x^2-24x-64=0 equation: 


Simplifying
3x2 + -24x + -64 = 0

Reorder the terms:
-64 + -24x + 3x2 = 0

Solving
-64 + -24x + 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 + -8x + x2 = 0

Move the constant term to the right:

Add '21.33333333' to each side of the equation.
-21.33333333 + -8x + 21.33333333 + x2 = 0 + 21.33333333

Reorder the terms:
-21.33333333 + 21.33333333 + -8x + x2 = 0 + 21.33333333

Combine like terms: -21.33333333 + 21.33333333 = 0.00000000
0.00000000 + -8x + x2 = 0 + 21.33333333
-8x + x2 = 0 + 21.33333333

Combine like terms: 0 + 21.33333333 = 21.33333333
-8x + x2 = 21.33333333

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = 21.33333333 + 16

Reorder the terms:
16 + -8x + x2 = 21.33333333 + 16

Combine like terms: 21.33333333 + 16 = 37.33333333
16 + -8x + x2 = 37.33333333

Factor a perfect square on the left side:
(x + -4)(x + -4) = 37.33333333

Calculate the square root of the right side: 6.110100926

Break this problem into two subproblems by setting 
(x + -4) equal to 6.110100926 and -6.110100926.


Subproblem 1
x + -4 = 6.110100926

Simplifying
x + -4 = 6.110100926

Reorder the terms:
-4 + x = 6.110100926

Solving
-4 + x = 6.110100926

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = 6.110100926 + 4

Combine like terms: -4 + 4 = 0
0 + x = 6.110100926 + 4
x = 6.110100926 + 4

Combine like terms: 6.110100926 + 4 = 10.110100926
x = 10.110100926

Simplifying
x = 10.110100926


Subproblem 2
x + -4 = -6.110100926

Simplifying
x + -4 = -6.110100926

Reorder the terms:
-4 + x = -6.110100926

Solving
-4 + x = -6.110100926

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = -6.110100926 + 4

Combine like terms: -4 + 4 = 0
0 + x = -6.110100926 + 4
x = -6.110100926 + 4

Combine like terms: -6.110100926 + 4 = -2.110100926
x = -2.110100926

Simplifying
x = -2.110100926


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.110100926, -2.110100926}

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