6x^2-8x-4000=0

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Solution for 6x^2-8x-4000=0 equation: 


Simplifying
6x2 + -8x + -4000 = 0

Reorder the terms:
-4000 + -8x + 6x2 = 0

Solving
-4000 + -8x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-2000 + -4x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-2000 + -4x + 3x2)' equal to zero and attempt to solve:

Simplifying
-2000 + -4x + 3x2 = 0

Solving
-2000 + -4x + 3x2 = 0

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

Divide each side by '3'.
-666.6666667 + -1.333333333x + x2 = 0

Move the constant term to the right:

Add '666.6666667' to each side of the equation.
-666.6666667 + -1.333333333x + 666.6666667 + x2 = 0 + 666.6666667

Reorder the terms:
-666.6666667 + 666.6666667 + -1.333333333x + x2 = 0 + 666.6666667

Combine like terms: -666.6666667 + 666.6666667 = 0.0000000
0.0000000 + -1.333333333x + x2 = 0 + 666.6666667
-1.333333333x + x2 = 0 + 666.6666667

Combine like terms: 0 + 666.6666667 = 666.6666667
-1.333333333x + x2 = 666.6666667

The x term is -1.333333333x.  Take half its coefficient (-0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
-1.333333333x + 0.4444444442 + x2 = 666.6666667 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333x + x2 = 666.6666667 + 0.4444444442

Combine like terms: 666.6666667 + 0.4444444442 = 667.1111111442
0.4444444442 + -1.333333333x + x2 = 667.1111111442

Factor a perfect square on the left side:
(x + -0.6666666665)(x + -0.6666666665) = 667.1111111442

Calculate the square root of the right side: 25.828494171

Break this problem into two subproblems by setting 
(x + -0.6666666665) equal to 25.828494171 and -25.828494171.


Subproblem 1
x + -0.6666666665 = 25.828494171

Simplifying
x + -0.6666666665 = 25.828494171

Reorder the terms:
-0.6666666665 + x = 25.828494171

Solving
-0.6666666665 + x = 25.828494171

Solving for variable 'x'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + x = 25.828494171 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + x = 25.828494171 + 0.6666666665
x = 25.828494171 + 0.6666666665

Combine like terms: 25.828494171 + 0.6666666665 = 26.4951608375
x = 26.4951608375

Simplifying
x = 26.4951608375


Subproblem 2
x + -0.6666666665 = -25.828494171

Simplifying
x + -0.6666666665 = -25.828494171

Reorder the terms:
-0.6666666665 + x = -25.828494171

Solving
-0.6666666665 + x = -25.828494171

Solving for variable 'x'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + x = -25.828494171 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + x = -25.828494171 + 0.6666666665
x = -25.828494171 + 0.6666666665

Combine like terms: -25.828494171 + 0.6666666665 = -25.1618275045
x = -25.1618275045

Simplifying
x = -25.1618275045


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {26.4951608375, -25.1618275045}
Solution
x = {26.4951608375, -25.1618275045}

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