6x^2-24x-80=0

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Solution for 6x^2-24x-80=0 equation: 


Simplifying
6x2 + -24x + -80 = 0

Reorder the terms:
-80 + -24x + 6x2 = 0

Solving
-80 + -24x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-40 + -12x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-40 + -12x + 3x2)' equal to zero and attempt to solve:

Simplifying
-40 + -12x + 3x2 = 0

Solving
-40 + -12x + 3x2 = 0

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

Divide each side by '3'.
-13.33333333 + -4x + x2 = 0

Move the constant term to the right:

Add '13.33333333' to each side of the equation.
-13.33333333 + -4x + 13.33333333 + x2 = 0 + 13.33333333

Reorder the terms:
-13.33333333 + 13.33333333 + -4x + x2 = 0 + 13.33333333

Combine like terms: -13.33333333 + 13.33333333 = 0.00000000
0.00000000 + -4x + x2 = 0 + 13.33333333
-4x + x2 = 0 + 13.33333333

Combine like terms: 0 + 13.33333333 = 13.33333333
-4x + x2 = 13.33333333

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 13.33333333 + 4

Reorder the terms:
4 + -4x + x2 = 13.33333333 + 4

Combine like terms: 13.33333333 + 4 = 17.33333333
4 + -4x + x2 = 17.33333333

Factor a perfect square on the left side:
(x + -2)(x + -2) = 17.33333333

Calculate the square root of the right side: 4.163331999

Break this problem into two subproblems by setting 
(x + -2) equal to 4.163331999 and -4.163331999.


Subproblem 1
x + -2 = 4.163331999

Simplifying
x + -2 = 4.163331999

Reorder the terms:
-2 + x = 4.163331999

Solving
-2 + x = 4.163331999

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 4.163331999 + 2

Combine like terms: -2 + 2 = 0
0 + x = 4.163331999 + 2
x = 4.163331999 + 2

Combine like terms: 4.163331999 + 2 = 6.163331999
x = 6.163331999

Simplifying
x = 6.163331999


Subproblem 2
x + -2 = -4.163331999

Simplifying
x + -2 = -4.163331999

Reorder the terms:
-2 + x = -4.163331999

Solving
-2 + x = -4.163331999

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -4.163331999 + 2

Combine like terms: -2 + 2 = 0
0 + x = -4.163331999 + 2
x = -4.163331999 + 2

Combine like terms: -4.163331999 + 2 = -2.163331999
x = -2.163331999

Simplifying
x = -2.163331999


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.163331999, -2.163331999}
Solution
x = {6.163331999, -2.163331999}

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